One of the more unique restaurants in that area, at least by my knowledge / experience which is little: El Charro Cafe or something similar that features carne seca. El Charro is pretty old, from 1922. Carne seca is kind of like finely shredded, reconstituted jerky. Barrio Brewing should be around there as well if that's of interest, though I don't know how that location is situated since I have only been to the one in Mesa (that one is cool because it abuts an airstrip!).
second that (El Charro), but I would not do the carne seca, too damned seca (dry)
try the birria, like brisket that falls apart. get a reservation a day ahead, or drink a margarita for 30 mins while you wait. very popular
going to Bisbee, get reservations for the underground mine tour, very cool
Titan Missile museum, outstanding. south of tucson 20 mins easy drive on freeway all the way.
San Xavier del Bac Mission, like an Ancient European Church out in the middle of the desert very cool, can buy frybread /chile beans right in front from the locals
Tomstone, on way to Bisbee, historical museum in the old County courthouse is the least touristy thing in town.
walk around Campus at the U of A, especially Old Main, historic building, and the center of campus, WWI memorial fountain on west side of old Main, for the students and alumni killed in the war to end all wars.
East side of old main is the outline of BB-39, USS Arizona, and memorial with names, rates, and hometowns of all 1177 sailors and marines killed aboard on December 7, 1941.
