I eat so well when we are at Disney World! Much better than when we are staying in town..sad really. ANYWAY!

Your vegetarian should have NO problem finding things to eat. Just make sure that the CM takes note that you have a vegetarian in your party when you made your ADR's. Some chefs will come out and speak with your vegetarian about what they like and what they offer and I have even had a few chefs walk me through the buffets and point out what is vegetarian and vegan.
Here are my picks for the best meals..
Table Service:
Boma - I love this place. I have never had a bad meal here and there is always more than enough for me to choose from.
Marrakesh - Yum! The vegetable cous cous is great! The vegetables remind me of my mom's cooking. Nice to have now that she's gone.
'Ohana - I've been lucky enough to have chefs come out and ask me what I like to eat and be more than happy to accommodate me. Plus there is always nibbles on the table that I can share with my family (salad, bread, vegetables, etc.)
Whispering Canyon - The food was really tasty and the atmosphere was a lot of fun!
Counter Service:
The Mara - Great counter service! I had the best veggie burger here. It was NOT the standard Garden Burger. This was flavored with cumin and other African type spices. SO good!
Cosmic Ray's - I love the condiment bar here. I can make my veggie burger just how I like it. The mushrooms are awesome!
Pecos Bill's - The salad they offer here can be made without the chicken. It is really tasty and refreshing. The jicama is a nice touch!
Sunshine Seasons - The food here is great. Plus they have really yummy desserts!
Regardless of where you go, your vegetarian should be able to have some great meals! Disney is so great about accommodating our meals.