Cafe Desta is my absolute favorite place to eat in Tucson. The vegan options are numerous and diverse, bursting with flavor, with an appealing presentation. The staff is friendly and genuine. The modern yet Ethiopian atmosphere lends itself well to romantic dates, girl's night out (in the extended dining room), family dinners, business lunches, or a quiet meal alone. A nice perk is that you are welcome to bring your own bottle of wine, and there's not a corking fee.
Note: While the food, soup, and bread are phenomenal, I don't often see vegan desserts offered here.