Bjclarke

First advice I can give you is make a list of what are the most important things for you to and make sure to save some time to enjoy the beautiful ship. I only say this because we booked excursions in every single port and I felt like we left no time to explore the ship and there is so much to see, there were things I found to do on the ship that I didn't know till the last day which was our sea day. 
For the excursions we ended up booking through the cruise line only because it was our first time to Europe and we wanted to be sure to make it back to the ship with plenty of time. If I go back I will use "Rome in a Limo" I researched them before going on the trip, they had great reviews and I saw their cars in all the ports through Italy. Also if you wanted to visit the Vatican I recommend booking a tour that includes a Vatican guide, they are incredibly knowledgeable and answered all of our questions. 

We set sail in 2 weeks and I've spent months and months planning our tours. We booked with a company called Joe Banana Limo/Italy Tour Sharing for our tours of Rome and Pompeii/Amalfi. Visit their site and you can book a tour for as many people as you like. The per person rate goes down, the more people you book.
If you find your "Roll Call" on the Cruise Critic website, you can recruit people to join your tour. We found this much cheaper than the ship's excursions and there are only 8 people in our tour groups. Many people on our Roll Call booked tours this way. At one point there was a spreadsheet with all the tours listed and web links (someone was very organized)! Now I've made "friends" with several of my fellow cruisers and we have a number of meet and greets set up. 
I can certainly share our experiences when we return!

It's also long because some of the European ports are really far from actual places you want to visit.  Caribbean ports you get off the ship and you're there. European ports you get off and you still have to take a train or some other form of transportation to get to Rome or Florence etc. 

I haven't yet done a Mediterranean or other European cruise yet (one day!!), but I think they typically give longer in those ports compared to the Caribbean because of the distances to reach many of the cultural or other popular tourist sites from the port.

Arrival time is when the ship docks; there will typically be around a 30-minute wait after that while the ship is cleared by the port before passengers can disembark. Given the early hour of all your arrivals, you'll probably want to also factor in time to have breakfast at the Windjammer (if you're in a hurry to get off) or main dining room (if you don't mind taking about an hour for sit-down breakfast with a menu and made-to-order dishes).
All passengers must be back onboard 30 minutes before departure time; the actual all-aboard time will be posted in your daily Cruise Compass newsletter. Do note that the times posted there are ship's time, which may or may not correspond to local time; be sure to check the time on a ship's clock or your stateroom TV, and make sure your watch / smart phone / whatever timekeeping device you use is synced up so you don't accidentally return too early / late. Several here make a point of carrying an analog watch that doesn't auto-update based on the current location, just to avoid potential issues like that.

I wanted to pass on a tip to try and reduce your cruise fare.  We are booked on Freedom for ABC Islands in Oct. for my wife & I.  Sunday is our final payment deadline.  Today before I called the travel agent to make our last payment, I checked the pricing on our Stateroom.  2B Spacious View Balcony on the hump deck 10.  3 days before final payment deadline it was $468 cheaper than when I booked it 18 months ago during a BOGO 60 sale.  One thing that Royal allowed was for us to change our deposit from refundable to non-refundable (don't need it for final payment) at the lower cruise fare rate.  We booked today under the standard BOGO 50 offering, no onboard credit.  Not only did Royal give us the lower fare they allowed us to keep the onboard credit from when we booked originally.
Cruise Hack #1 always check the available fare before making your final payment and if you booked your cruise with a refundable deposit change it to non-refundable.  This hack just paid for one of our airfares to San Juan.