What type of vegetarian dishes do you like? That's probably going to be the best determinant of your answer. (I'm more of a pasta or "modified apps" kinda girl than a "plate of veggies" kind of girl, so that makes a difference.)
I'll think on this - nothing is sticking out as "best" in my mind. I've had perfectly satisfactory meals at Grand Floridian, Captain's Grille, Kona, 'Ohana, 1900 Park Fare, Beaches & Cream, Flying Fish, Rainforest/T-Rex... lots of options. Wave sounds good, but haven't made it there yet.
In the parks, I think my current favorite is Spice Rd Table. Their hummus & olives is to die for!