Tusker House has an excellent veggie sandwich
Last fall, they had a an awesome veggie sandwich on focaccia bread, but when we were there last month, they had changed it to this barely edible thing in a pita that was yucky. My favorite counter service restaurants are Columbia Harbour House at MK (great hummus sandwich and veggie chili) and Tangerine Cafe at Epcot.
I'm vegetarian and have always hated that Tusker House veggie sandwich. It sounded so good and even on the focaccia bread, it was just soggy and icky - I even tried it again in case the first had just been sitting around. Never again. LOL
I will second the vote for CHH, though. That sandwich/chili combo was just excellent and I am really looking forward to it when I go back.
One other vote.... when we did Lunch with an Imagineer at the Brown Derby and the chef made me a special dish since the set menu was all meat-based. It was a coconut-crusted Asian tofu dish. Let me tell you, I HATEHATEHATE tofu and this dish was really good. I suspect that most places will be able to do something similar if you don't see something on the menu.
Mama Melrose also had a nice penne in tomato-vodka sauce. Mmmmmm.
Enjoy!