DublinFC

I cannot say that I am an expert at NYC and traffic in the area.  For that I am going to tag @KathyC @ellcee and @JLMoran on that one.  I can however tell you about both our experiences from sailing out of NJ in March 2018 and July 2019.
In March 2018, we had no desire whatsoever to see the city.  We flew into EWR and stayed at Embassy Suites in Elizabeth, NJ.  It is close the airport and roughly about 20 mins to the port.  Cape Liberty is located in an industrial area and there are not really any hotels within the vicinity.  It's not like sailing out Miami or Fort Lauderdale.  We found Embassy suites to be excellent for what we wanted.  It's clean, modern, right across the street from a shopping outlet, they have a complimentary airport shuttle, complimentary breakfast and happy hour and spacious accommodations as all rooms are suites.  They also offered shuttle service to the port the morning of, but we did not take it, we usually use ride share instead.  I don't like waiting around for shuttles to load and with 4 people, it is more expensive because you pay per person.  I would not hesitate to stay here again if all I wanted was to get on the ship.
In July 2019, we still flew into EWR, but we stayed in Manhattan this time.  Because we had the time, we went two days prior to cruise to explore NYC with our kids.  Initially, we had Embassy Suites booked again but in thinking about it further, we decided to cancel the booking and stay right in the heart of Times Square.  There are some who will tell you that it is still better to stay in NJ and just take that PATH train to explore the city but for us, we like the convenience of just starting our day right in the city and not have to worry about getting into the city and then back out of it at night.  We booked at the Intercontinental Times Square (this trip was documented here) and thoroughly enjoyed our stay there.  It cost us about $100 for the ride into the city and about $100 to the port the morning of the cruise.  Seeing that there were 4 of us, I did not find that to be ridiculous. There was minor traffic both ways but from what I know, that can really vary depending on the day and time.  Going into NYC, our plane landed around 2pm so we ran into minor rush hour traffic.  The morning of the cruise, we left our hotel just after 9am, and there was not much of anything heading into Cape Liberty.    As far as time goes, it was just under an hour each way.
This summer, Hubby and I are sailing out of Cape Liberty again (but on Adventure) and we have once again decided to stay at the Intercontinental Times Square because we are going to catch a Broadway show pre-cruise.  Hope that helps.
 

That is what I wanted to do but Hubby wanted to see the ship pass under the bridge. ?
I agree.  Airfare is cheaper to Newark than to Florida usually but still not enough to make me want to sail out of there in March again. 
We enjoy sailing out of NJ in the summer though.  Last summer for the GC, we spent a day or two in Manhattan and loved that.  This July, when it's just Hubby and I, we plan to do the same.  Stay and do a few things in Manhattan before heading out on Adventure.
Totally hijacking the thread now lol...sorry

I agree twangster regarding the choke point.
Will say I see the Bionic bar and Wonderland as been there done that and collected the check.  The Bionic bar just doesn't grab me.  I do love the 270, especially when it comes to the Quest.  I think it is the perfect lay out.
As my husband loves to tell me, I am navigationally challenged.  It was easy for me to navigate the ship, as big as it is, within a day I knew the quickest way without using the elevators to get to where I wanted.  As much as the Esplanade is not my favorite, we always enjoy it from a people watching aspect.  Get a slice of pizza and watch people walk by...just remember that smell of popcorn will cost you $$$.  
Without a doubt, Bayonne is my favorite.  From dropping off your bags with the porter to stepping on the ship, I don't believe it has taken us more than 25 mins.  The real reasons it is my favorite, is tied to me personally.  I love the 9/11 Memorial at the port.  @DublinFC  I am not talking about the 9/11 Memorial.  This is a beautiful teardrop made out of the steel from the Twin Towers aka World Trade Center.  It was gifted by the Russian Govt.  The 2nd is, as a Jersey girl, the Verrazano is a big deal to us.  The Anthem only clears the bottom of that bridge by 30 or so feet.  Thus, when you are up on the pool deck,  you actually can hear the tires whizzing over your head....okay let's be real, no whizzing by, just the horns honking and looking at the brand of the cars tires.  Thirdly, if you have a balcony, and are an early riser, get up the day you will debark.  Pulling back into Bayonne, and seeing the night lights, including the Statue of Liberty is awe inspiring.  It is unique.  
We will be sailing out again next summer, but on Oasis.  After that we will be flying to Miami.  Nobody flame me.  I just don't like sailing out of Miami.  Nothing against the port.  Everything against how I hate the Miami airport.  I am seriously thinking about going into FLL, that is how much I hate that airport.  I know Atlanta always ranks in the bottom for airports, but my husband and I believe that is only because those that grade airports never went to Miami.
@DublinFC  Make sure you also book your NorthStar for the 1st days of the cruise.  The reason why is the same as the acrobatic show.  If the seas start rocking, they may not send up the NorthStar.  You can also pre-book the IFly, but the seas, to the best of my knowledge has an impact on whether it is open or not.
 

I've never sailed out of Bayonne in April, but we've sailed out twice in October. Once in mid-OCT and once in late OCT through Halloween. 
At that time of year, it's light jacket/sweatshirt weather out of NY. We did not notice rough seas going down on either sailing (Explorer and Liberty), but in both cases it was rocking noticeably late evening/early morning on the way back. My wife joked on the Explorer cruise that she felt like a baby being rocked to sleep! I think part of the reason we had so much motion is because they were trying to make good time back into Cape Liberty.
 

Everytime I return to Anthem (or Ovation) I feel good. 
Yes the Esplanade can be a choke point at times but at least there is the Bionic Bar/Wonderland bypass one deck up to get fore or aft to avoid the Esplanade.  Voyager and Freedom class isn't exactly a picnic during the 2 for $20 sale either but no bypass except through cabin halls so...
Oasis class is great and all but I really like Quantum class.
As someone who loves sea days, the days up and down the coast don't bother me.  
Before sailing from Bayonne I once said "Who in their right mind would fly to Bayonne to cruise when you can fly to Florida and cruise?".  Since then I've done a number of cruises from Bayonne including a B2B on Anthem in the winter.  That's four sea days in a row with a turn around day in NJ snow flurries.  I loved it.  
I'm actually really looking forward to going back to Anthem very soon.  

Hopefully mid-April should feel more spring-like and with calmer seas for you.

The thing to also remember regarding Anthem, is that they have an indoor pool plus the Solarium and the outdoor pool.  Thus, for pool options, it is not outdoor or nothing.  If it is just you and your wife, you will LOOOVVVEEE the Solarium on Anthem.   It is not only a great set up, but the Solarium Bistro is connected to it.  You will also love the WJ once you get into warmer areas because it has an outdoor eating area.  
We actually sailed on Anthem as it skirted not one, but 2 hurricanes.  It was only one day that the ship was really rocking.  Our cruising partners tend to get motion sickness and wear a patch, they were fine.
We typically try to sail out of Bayonne over Miami since we can drive to Bayonne.  There is nothing like going under the Verrazano bridge, nor being able to see the Statue of Liberty in the distance from the ship.  
Last summer we did Adventure out of Cape Liberty.  I want to say that we were somewhere on the NC/SC border by early/ mid-day on the 2nd day.  That itinerary had us doing 1 sea day and arriving in Bermuda on what would be considered day 3.  
Anthem is a nice ship.  The true negative I have with Anthem is that it has an Esplanade, not a Promenade.  It can get a little packed from a traffic flow compared to the Promenade style. 
Make sure you book the acrobatic show (can't recall the name) that is in the 270 for the beginning of the cruise.  We booked The Gift, We Will Rock You and the acrobatic show in that order.  Unfortunately, the night we had for the acrobatic show, was at the end of the cruise and they canceled the show.  However, we were not too disappointed.  The only place to get the Kummelwreck sandwich is in the 270.  If you go @30 mins before lunch ends, the acrobatic crew comes out to practice for the show that night, not using music.  We sat there after we finished our lunch and watched them go through their show..  At least we got to see them perform ….somewhat.
If you have to miss any of their shows, everyone will tell you, miss The Gift.  I.000.000% agree.  Make sure you stay until after the actors take their last bow for We Will Rock You.  In other words, let everyone rush for the door, stay in your seats.  
 
 

I’ve done Anthem in November, December and January.  I’m going again this coming January.  
It starts and ends with “long pants days”.  Lots to do, works for me. 

Don't forget, Anthem has a lot of indoor activities that you can participate in, including a covered pool, so you are not really missing out on anything other than getting a tan.  

I totally get not being able to predict the weather, especially so far in advance ?. We decided to book it and take what Mother Nature throws at us. We both think Anthem will be a better fit for us and we found a great price though our TA. 

Update 12/30: So we just returned last week from our amazing cruise on the Mariner! Day 2 we arrived to Cococay (about 77 degrees that morning), and my husband and I were the first to arrive to the swim up bar (like kids in a candy store). My hubby went right on in, and I was barely tip toed in and wasn't sure I could make it. The bartender, laughing, was like "Come on in! I'll warm you guys up with a drink when you get over here!" I threw myself in all the way, and swam to the bar where a nice stiff shot and a CocoLoco was waiting for us! Incredible experience. The water was cold, especially until the sun came out not long after. It ended up being a beautiful, warm 85 degree day! The island is truly incredible and very well done. We were excited for the return back on day 4, unfortunately, due to the weather we were unable to dock. I can't wait to go back soon! 

Good to know, thank you!

It has been my experience that the seas out of Bayonne can be rough...no matter what time of the year it is.  I wouldn't think that it would be bad enough to abandon your plans to sail out of Bayonne though.   Even though there is always a possibility of spring storms, I would think that April would be on the safe side, as far as months to sail out of the NY area.  We hit a nor'easter a number of years ago sailing out of Bayonne and had one hell of a rough few days but I don't think you have to worry about that in April.  I think you would be a-ok.

Just don't see it happening in my cruise lifetime.
I also don't see them charging for the MDR or WJ either.  
If they ever tried to charge for all food at their private destination it would send everyone back to the ship to eat.  They know that.  One way or the other Royal is feeding the ship's population on the day the ship is at a private destination.  
I could see them charging for some entrees at the Snack Shack.  Kind of surprised they didn't out of the gate.  So that could become a paid venue in my cruise lifetime. 

I stayed at the Best Western Fort Lauderdale Airport/Cruise Port a couple of times. It has a free shuttle to the hotel from the airport and free continental breakfast. There is a shopping center across the street with a Winn Dixie, liquor store, restaurants, and a few other stores (perfect for last minute things).
It's about a 12 minute drive to the port. However, they charge approx $15 per person for a shuttle to the port that doesn't leave until after 10AM. We never had a problem with lyft taking us to the port.

All I have heard is that on the island is that you can eat and drink (with package) and enjoy till your heart is content without spending any extra money.  Yes there are options to spend money on, but that is to be expected.  It does not mean you have to spend the money.  It is a choice.

@twangster thank you for all the wonderful photos.

All I have heard is that on the island is that you can eat and drink (with package) and enjoy till your heart is content without spending any extra money.  Yes there are options to spend money on, but that is to be expected.  It does not mean you have to spend the money.  It is a choice.

All I have heard is that on the island is that you can eat and drink (with package) and enjoy till your heart is content without spending any extra money.  Yes there are options to spend money on, but that is to be expected.  It does not mean you have to spend the money.  It is a choice.

We stayed at the Hilton FL Marina on the 21st using points. Our rooms weren't ready until 4:30 and 5:30, and there is a lot of construction/renovation going on. (Lots of people sitting around the lobby waiting for rooms!) Rooms were nice though, and they gave us a free breakfast to make up for the troubles. 
The other hotels mentioned are in a better location for last minute shopping at Publix, etc. 

Most menus are available on the app now.

Ooops, thank you, forgot about that option.

This is all really good info, thank you all so much!

I think any one of the hotels in that 17th street cluster will suit your needs. I prefer the Hyatt Place myself - rooms are for 4, but could easily fit 8 - and like Embassy Suites and Holiday Inn Express it's close to a large cluster of restaurants, plus a Publix, Total Wine, Ross and Dollar Store for those "I forgot to pack" options. And wine. Price is $130/night in the late spring/summer if you go through a 3rd party site (don't know what board policy is on mentioning other sites, so not naming it here).
All of these places are a short taxi/Uber ride away from port. No shortage of those going around the area on cruise mornings.

I just booked a room through Booking.com over the weekend. The prices were decent.