Hi Monsie, my boyfriend and I went on a short cruise to the Bahamas about a year ago and we just wore jean shorts and tank tops (for me) and t-shirts and cut off shirts (for my boyfriend). We are in our early 20's so we don't have to dress "appropriate" if we don't want to. I went to dinner on the informal nights in shorts and tank tops, I don't think it matters, whatever is comfortable. We're going on another cruise this coming May with my parents and my boyfriends parents (they're all around 50) and I'm going to tell them to bring shorts, jeans, t-shirts and tank tops, as I am telling you. But as the other poster said, jeans may be too hot, depending on when you're cruising. I probably won't be wearing jeans when we go to the Western Caribbean in May, but in December, I'm sure it would be fine.
Hope this helps and have a great time!! (it's going to my parents and boyfriend's parents first time cruising as well!)