My husband and I went to WDW before we were married (which means without kids!) and we had a fantastic time. We stayed at the Yacht Club, which was really nice. If you can afford it, dinner at the California Grill is terrific food and an unbelievable view over the entire Magic Kingdom, which is especially magical at night. Very romantic. You can also just have a drink there. We also enjoyed going to Epcot at night for dinner at different restaurants in the World Showcase. San Angel Inn in Mexico is lovely, and we also liked the Japanese restaurant, Teppanyaki Grill. Don't miss the fireworks at each of the parks-- they are all different and unique, the best fireworks displays you will probably ever see.
I agree with everyone else about waking up early (you can always go back to your hotel for a nap later on) so that you can see what is most important to you before the big crowds. Also visit the water parks-- Typhoon Lagoon and Bllizzard Beach are very different from each other and a lot of fun.
There is a specific Birnbaum book on WDW without kids, and it's a great book. I like the Unofficial Guide too, but this Birnbaum lists a lot of romantic types of things to do that aren't in the other books.
Don't avoid things like character breakfasts-- they are fun wven without kids. We like Chef Mickey's for dinner (in the Contemporary). The attractions and rides intended for little ones are also worth seeing, once the "must see" things are out of the way. Don't miss the Muppet 4D movie, for example, or Honey I shrunk the Audience. Or the Teacups!
If you give a little more information about what types of things you and your husband enjoy, people can probably offer more specific suggestions for you.
Another thing: take a car service from the airport to your hotel and back. For two people, it costs about the same as the Mears shuttle bus and you can zip right to WDW without waiting for the bus to fill up and make a dozen stops before you get to your hotel. If you call Tiffany Towncar, they'll meet you at the baggage claim and they'll even stop at a grocery store on your way to WDW so that you can stock up on snacks. (It's $90 roundtrip, I think).