As a cruiser that is headed on their 4th cruise and 2nd time with RCC by choice, I can tell you you will see people in slacks and tops at most evening meals, on the formal night and if you are cruising 7 days or greater, there are 2, you will see everything from tuxes and evening gowns to dressier sun dresses etc. I myself like to dress up for dinner everynight and take one long dress and one cocktail dress for the formal nights. I have worn sun dresses, skirts and tops other nights as I am not a slack person but you will be ok in whatever makes you comfortable as long it is not denim, shorts or bathing suit. Some wear capris with a dressier top as well. The dining room is very formal looking like a fine dining restaurant. If you go to the other restaurants it is probably more casual. I like to eat in the dining room 3 times a day. Most do not.
Hope that is helpful. Remember they take pictures on the formal nights that are very nice and are reasonable so it is an opportunity to preserve the moment and the memories.