I lived there for a couple of years in the early 90's. Luckier gave a good answer. Lots of restaurants and thrift shopping around 4th Avenue.
I'll add a few more things ...
On the (modern) US history front, you can check out the Titan Missile Museum. It's an old missile silo buried in the desert that you can go down into. Very creepy.
And, if you want to make it a military themed day, also check out the Pima Air & Space museum, where there are hundreds of old aircraft mothballed in the desert. Apparently, the military puts stuff out there because it never rusts.
I'm not sure what you mean by "reasonable" distance, but Bisbee is an old copper mining town that is 90 or so miles away. On the way, you'll pass through Tombstone (of Wyatt Earp and gunfight at the OK Corral fame). Definitely on the touristy side, but worth a visit.
For live music, check out Hotel Congress in downtown Tucson. Meat Puppets there on Dec 30th! (if that's your cup of tea, it would be mine).
For authentic food, the Mexican food in Tucson really can't be beat. There are a thousand good places, with the most authentic (along with less expensive and less crowded) on the south side of town. Mi Nidito is an old favorite. Christmas is also tamale season, so don't miss the green corn tamales. It's not uncommon to see little old Mexican ladies going from bar to bar selling them out of ice chests. Probably $5-10 for a dozen. Buy some.