There are lots of options for (as my husband calls it) "selective eaters" at Disney World, and certainly many that are romantic and lovely.
My first suggestion would be the Yachtsman Steakhouse for the best steak on property (the best steak I have ever had, honestly!). They also have chicken dishes, wonderful salads, and a fabulous wine list.
Another favorite of ours is Artist Point at the Wilderness Lodge. I know the menu can look a little scary (with the Surf and Turf being a buffalo tenderloin and salmon), but my "meat and potatoes only" husband loves the restaurant. They always have a wonderful steak dish, and I know that I have seen chicken on the menu. Again, an incredible wine list. If you are into wines, try the cellar flight (three small glasses that match your dinner selections).
Another place you might want to check out is Citricos at the Grand Floridian. Great food, great wine, and a wonderful atmosphere. Ask about a view of Wishes (fireworks) when you make your reservation.
Artist Point is usually a bit quieter than Yachtsman - I think it is the location more than anything.
Both resorts also have gorgeous grounds to walk after dinner. If you go to Artist Point, stop by and see the geyser in the evening after your meal.
Have a great time, and enjoy your night out together - wherever you choose to eat!
Catherine