I'm not a big fast food restaurant fan, but there is one place that I like that you could consider fast food. I am a fan of Panera Bread! They do offer some vegetarian and vegan options, and I'm addicted to to their unsweet iced tea.
Had lunch there the other day and this is what I got... the Mediterranean Veggie sandwich, minus the Feta cheese, and black bean soup. Yum! Oh, and the unsweet iced tea of course. When it comes to the breads, you can always substitute one kind for another. Check out their site to find a bread you'd like to have or that meets your dietary requirements (they provide the ingredients online). Panera Bread also has a wonderful strawberry poppyseed salad every summer (minus the chicken, of course). Great salad!
Sometimes for breakfast I also stop in and have a bagel at Panera Bread. Some of the bagels are vegan and some are not. However, they provide all the ingredients right on their site, so it's easy to determine which are vegan. The vegan ones do include sweet onion poppyseed and everything, as those are the ones I usually get. What do I top it with? My own vegan cream cheese or hummus. Yum!