Gee, where to begin?
We don't have kids, but go to Disney regularly.
World Showcase is great to do as an adult! Take your time walking around at all the different countries and sample the excellent adult beverages each has. Stick it out until Illuminations for a wonderful finish to your day.
We love walking around MK at night. That's when it's most magical for us. We always do the late night EMH's there, as there are less kids by the late hours and you can walk on a lot of the rides. We always have a blast. You can ride Pirates over and over!
And we love AK. Going as an adult, you can really take your time in all the animal areas to talk to the CM's and find out more about the animals. I love learning all kinds of interesting facts, and the AK CM's are full of great information. I've learned that many of the bats are on glucosamine (sp?) for their arthritis, that all the tigers are sisters and that's how they can live together without territory issues, and that there are new break through's in heart care involving tarantula venom! And on my last trip two weeks ago, I got to observe surgery on a rat!
(Yes, I know some of these things are NOT romantic, but it's something you might not be able to do if you had kids along with you.)
Dining at Disney is a very important part of our trip. We love trying out the signature restaurants, which can be very romantic. I highly recommend California Grill and Jiko!