I would definitely recommend reading the FAQ on this part of the forum as it has loads of great tips!
In the Bahamas I wouldn't really recommend anything. Personally I like to use this as an extra day on the ship but its totally up to you.
Definitely try and do a lunch in the main dining room at least once when onboard as I always find the sit down lunches great.
I would also be inclined to think about doing a drink tasting on your sea day as these are so much fun and relatively cheap ($20-35 each depending on what type). These you book while onboard.
As its your first time onboard I would actually not recommend a dinner in the "adult" restaurants unless you really want to try it. I would however recommend a Brunch in Palo. These are bookable in advance (which for you will be 75 days before sailing assuming you have paid in full) but they might show online as fully booked. Don't give up though! When you get onboard go and try and get a reservation as soon as you can (it will be listed in the Navigator you get in the port that tells you whats going on) as they keep quite a few for when people get onboard.
Don't be afraid to ask for extras at dinner - like two portions of something if you really like it. Also as all the food (apart from the adult restarants which carry a premium) is included try new things and then if you don't like them order something else (or there is always room service or quick service for later).
Definitely look on
http://www.disneycruiselineblog.com for recent 4 night navigators that way you can see what is usually offered and get an idea of the things you would like to do. But remember, you can never do everything you want and you are meant to be relaxing! On my recent 14 night cruise I had a list of 44 things I wanted to try based on recent cruises on the same ship and I think I managed about 15-20 of them if that. It just means you have a reason to go back.