There is a pizza parlor and a cafe on the promenade with food that is included in your cruise fare. The cafe does have some extra-fee items too. It is open 24/7. The pizza place has more than pizza on the menu.
Not only can you eat breakfast and lunch in the dining room, I urge you do try it - especially for breakfast. Don't become a slave to the buffet!
Rockets has a $4.95 per person cover charge. For this you can eat all you want. They do have some ice cream specialties that cost extra but I've never seen a reason for getting them. They'll shower you (not literally) with onion rings and fries and frankly over-feed you. I once had a waitress make a mistake on the order and she brought me a double order of everything! I think I skipped dinner that night.