Disney is wonderful about accommodating dietary restrictions, including offering vegetarian and vegan options. At buffets, this means a cook will come out and tell you what you can/can't have from the buffet. At a la carte table-service restaurants, they will customize a meal for you, if necessary. (Details here:
http://www.disneyfoodblog.com/2011/01/20/a-vegetarian-in-disney-tips-from-an-expert/)
It's up to you which style and price point you'd rather do, but Disney will work to satisfy the vegetarians in your party no matter what.
Some of my suggestions (some are repeats from those mentioned by others in prior posts) would be:
- Hoop-Dee-Doo Musical Review (Fort Wilderness, Wild West musical dinner show; the advertised menu includes chicken and ribs, but vegetarian options will be provided on request)
- Be Our Guest (Magic Kingdom; CS at lunch and TS at dinner; French-inspired food in the Beast's Castle)
- Tangierine Cafe (Epcot CS; Moroccan tabbouleh, shawarma meats and baklava - vegetarians would have to embrace the lentil salad)
- Sunshine Seasons (Epcot CS; multiple stations, something for everyone)
- The Crystal Palace (MK buffet; multiple stations, breakfast lunch and dinner with Winnie the Pooh and friends)
- Sanaa (AKL, Indian a la carte), Boma (AKL buffet), or Tusker House (AK buffet with Donald Duck and friends)
- 'Ohana (Polynesian, all-you-care-to-enjoy), although the advertised dinner includes meat skewers, there are vegetarian options that the chef will send out on request