I live in downtown SLC, and there are quite a few places around here...
A couple that immediately come to mind:
-Omar's Living Cuisine
-Long Life Vegi House
I have been to all of these places and absolutely love them! Sage's and Oasis being my favorite. All of these places are in/near downtown....
I am pretty sure they all have websites. Also, almost all of the restaurants I have gone to, have no problem accomodating a vegan/vegetarian diet. Everyone is pretty friendly around here!!!