While not outside Chicago, the Oasis Cafe is definitely off the beaten path. It is on Wabash Avenue, just north of Madison. However, it is "hidden" at the back of a jewelry store. The food is outstanding and since it is middle eastern there are lots of vegetarian/vegan options. The falafel sandwich is outstanding and the hummus is really good as well. They have limited seating and it fills up during lunch.
I'm not a vegan, but saw this post and had to comment. My boss and his wife are vegan. I went into Chicago a few weeks ago with him and stopped for food. We stopped at The Handlebar and had some amazing food. It's not off the beaten path, but it's great food.