Which cruises are best for younger (late 20s) couples?

Hi, we're a 27 and 28 year old couple and we want to go on our first cruise while passing through the US (on the way home from the UK) in early/mid March. We're thinking Carribbean is the obvious choice, niether of us has been there. Celebrity or NCL 7 day ones look good but our main concern is that our cruise will be mostly seniors or families with small children. We also would prefer shore trips with some kind of cultural experience rather than just beach resorts. We enjoy good food and wine, and a good night out without too much of a hangover. Any recommendations (or warnings!) from personal experiences much appreciated.