Hi Megan_Rae, Bahamas is really, really expensive; especially food. You can walk to Junkaroo Beach, it's a free public beach about a 15 - 20 minute walk from the port. It gets really crowded later in the day so if you can get off the ship early and get there early, you'll be okay. You can rent chairs and umbrellas, or obviously skip that and bring towels from the ship. If you are really on a budget, I'd suggest bringing some Ziploc baggies and saving some emptied water bottles (or get each kiddo one from the dollar store) and pack yourself some lunch and snacks because like I said food is really expensive; for a family of four you could easily spend $100 on burgers, fries, and sodas for lunch. When my kids were younger, I would bring new blow up floaty toys (like rafts, rings, or balls) and stuff like that from the dollar store, then just leave them at the beach with the porters. As long as you plan, you can pull off a free (or relatively free) beach day in the Bahamas. Just google Junkaroo Beach.
As far as Cococay, it's another beach day, so again, plan on bringing sand toys, floaty things for your kids, etc, and you'll be good to go. Chairs, umbrellas, food, and drinks are free there, and there is lots to just walk around and look at!
Hope you have fun!