There's so much for adults to do at WDW without the kids! (My husband and I don't have children but love going to WDW.) We really enjoy a leisurely afternoon or evening at World Showcase at Epcot, stopping for a glass of wine in France, maybe a beer in Germany and just soaking up the atmosphere with no agenda otherthan to enjoy our time together.
Any boat ride at Disney is great, but if you can swing it, the boat from MK to the Wilderness Lodge (or the WL to the MK) at night can be really special. Another romantic option is hitting the beach at the Polynesian in the evening. I'd also recommend a morning at the Grand Floridian Spa if it is in your budget -- bliss!
One of the things we love about WDW is that there's something wonderful to see at every turn. Take time to enjoy things like lingering over a glass of champagne in the lobby of the Grand Floridian, really exploring the Oasis at Animal Kingdom, hitting the hot tub after a long day in the parks, stolling around Crescent Lake holding hands -- well, you get the idea.
As others have said, don't miss having a dinner or two at WDW's signature restaurants. They are all special in different ways and you really can't go wrong. We really like Flying Fish on the Boardwalk (the food is fantastic as is the service; plus you can then head out to Jellyrolls), the California Grill at the Contemporary (even if the food wasn't delicious we'd go for the MK fireworks view) and the Brown Derby at Hollywood Studios (also great lunch, especially when you need a midday break).
You'll have a wonderful time!!