If you want more than just one choice, I think Boma and Tusker House are your best bets (I haven't tried Tusker House since it was changed to buffet, but I've heard it's got lots of veggie options).
Most table service restaurants have only one vegetarian choice on the menu or nothing on the menu and you need to ask for the vegetarian menu (which in my experience has been only one or two items) or there isn't even a vegetarian menu, but there is some option the chef can make you.
Table Service restaurants that I think have tasty options even if there isn't more than one or two vegetarian choices at each:
San Angel Inn at Epcot
Brown Derby at DHS
Le Cellier at Epcot (off and on...they change their menu a lot and at times their veggie option has been either the best meal I had all vacation or something not to my taste at all).
Jiko at AKL
Crystal Palace at MK
Mama Melrose at DHS