Suggestions to first time cruisers:
1. Take the ship's tour, usually offered right when you board before you can get into your rooms
2. Ride the Aqua Duck at least once!
(for some of us, once is enough)
3. Play the interactive games that take you around the ship to view all of the special "paintings" - it's not just for kids!
4. See the shows - Disney has the best shows on the high seas!
5. On a 3-night, eat in all 3 dining rooms (as you said), and save the fancy/paid ones for next time (you will be very sad if you miss your rotation for Animator's Palate)
6. Bring some Highlighter-type pens so you can highlight the activities you want to do each day from the Personal Navigator (and go to Guest Services to pick up extra ones so you don't have to share Navigators)
7. Have fun!