First cruise - take it all in. Try to get as early a port arrival time (PAT) as possible so you can get most time on the ship! If you might get seasickness get a patch to put behind your ear or buy some SeaBands!
Some things I would say you can do:
1. Eat dinner in the main dining rooms each and every night. It's a full on 4-5 course meal with usually great servers and a great time. The rotation is not that important. If you have food allergies please make sure they know that as soon as possible. We never skip a main dining room meal on any
Disney cruise and we have been on 8 so far.
2. Walk the ship. Just take your time. Walk it. Up and down both sides. Explore the ship. Just so much to see and do.
3. Go to the evening shows opposite your dinner time in the Walt Disney Theater. Those are typically Broadway style production shows and a lot of fun.
4. Dress up if you want and get your pictures taken. Around the holidays, picture lines do start early say 5 pm for early seating and just keep going. So get there early if you want.
5. Ride the AquaDuck on the Dream if you can at least once (more if you like it of course)
6. Order room service at least once - even if just a morning coffee with pastries to enjoy on your balcony. (it's included except for select items) and this order you can actually place the night before you go to bed so it will arrive whenever you want in the morning!
7. Even thought just adults, check out the kids club during open house and do a quick walk through. Neat to see the offerings.
8. Have a soft serve ice cream from deck 11. Yum!
9. If you want a souvenir or something try to buy on the first day! supplies dwindle as the sailing continues.
10. If you are going to scrapbook your cruise, take notes during the day so you have them for scrapbooking later on when you have your pictures etc.