My husband and I took our first three Disney cruises before we had kids. There is lots of evening entertainment (though as night people, we found that really, the ship pretty much shuts down after midnight, which can be a bit off putting if you're generally up til 2, but you have to get up EARLY on port days at any rate). There's the adult pools, Cove Cafe (which, frankly, is my preferred place for breakfast because PASTRIES), the movie theater when it's not showing a kids movie, the spa, etc. During the day there are a lot of activities geared towards adults, like trivia contests, ship tours, wine tastings, art auctions, bingo, and the like. On occasion they even have dancing lessons. And of course there's Palo brunch and dinner, and if you're on the Fantasy or the Dream, there's Remy. Do not skip Remy.
My husband was worried before our first cruise that he would be bored and find it hard to find something to do. By the morning of the second day he admitted that was not the case. You can do as much or as little as you like. My favorite 'adult activity' was often 'lounging on the outside deck with a book and a glass full of the drink of the day'.
