Hi, Jenny.
Some suggestions for a romantic dinner:
If you really want to splurge, go for Victoria and Albert's. The food is fabulous, the service is wonderful, and the setting is beautiful. It isn't cheap, by any means, though. The menu is different every night, and it is fixed-price. You aren't stuck with only one option for each of the six courses, though; there are a few choices for each (except for the amuse bouche, which starts the meal). If you decide on V&A's, go ahead and splurge for the wine pairings, if you are wine people. At $60 a person for 6 pairings, it is actually quite a good deal.
If you want somewhere with wonderful service and food, that isn't a fixed-price menu, so that you have some options for controlling the price, I would recommend Artist Point. My husband and I go there every visit to WDW. While some may recommend California Grill, I find Artist Point to be more quiet and conducive to actually spending time talking to the person(s) you are dining with. They have a very nice wine list from the Pacific Northwest to add to the always lovely menu.
I would steer clear of park restaurants, and from the "monorail resort" restaurants other than V&As since they are likely to be full of families (and the resultant excitement of kids!). Let me be clear so that I don't become the subject of "hate responses" from parents - I am a parent myself, and even when we have traveled as just a couple, I have never minded appropriately behaved (even if totally excited) children around me at a restaurant. It is part of the charm of being at Disneyworld - it just doesn't scream "romantic" to me.
One suggestion: you may want to get opinions on the bistro on the second level of Chefs de France. I have not been in many years, so I can't remember whether it would be a good option or not.