There are SO many cool and romantic things to do at Disney. Some things that DH and I did were:
Dined in the castle our first evening there.
(Cinderella's Royal Table)
Went on a Wishes Cruise.
Dine while watching Illuminations in Epcot.
(I think this was Dh's favorite)
I would agree with the other poster who mentioned taking a horse drawn carriage ride. We had one of these planned, then we ended up cancelling once we got to WDW because we wanted to use that time to spend with our families before they left and didnt want to feel rushed. We didn't think it was a big loss seeing that we already rode in cinderellas carriage the day before, but this is still going to be a must do for our anniversary trip. You can get these carriages at POR and Fort Wilderness.
O one more thing that we did on the spur of the moment was to rent one of those mouse boats at the resort. They let you go out for 30 minutes and you can make it a relaxing ride, or a fast ride!
Enjoy!