Romeo Void at the University of Arizona Student Ballroom. The guitar, bass, drums and sax of this band were really locked in and was mesmerizing. I also saw the Talking Heads and Ramones at the same location but Romeo Void was best.
Jonathan Richman and the Modern Lovers at a club. Before he went it alone, Jonathan had two band members and he did a really long set and was just fantastic.
Violent Femmes at the University of Arizona Cellar. I was a student and just went there to eat and this was a free concert set up that I had no idea was happening. First album VFs. They had fun and were playful and great. A wonderful surprise.
I also saw The Kinks, Ray Davies by himself, The Church, Aimee Mann several times (she was excellent), The New Pornographers, Blue Oyster Cult, Bruce Springsteen (thought it went on way too long), Thin White Rope, Spoon, The Cure, Crowded House, Meat Puppets, Elvis Costello, Arlo Guthrie, Iggy Pop, TSOL, Punch Brothers, Chris Thile solo, Snakefinger (a nice concert), Diane Schuur (got kicked out of the bar because I didn't drink although I bought the 2 drink minimum sodas), Fishbone, Wednesday Week, Richard Thompson, Pere Ubu, Deer Hoof, Of Montreal, and local Tucson bands such as The Giant Sandworms (then Giant Sand), Street Pajama, and The Serfers (before some of them became Green on Red).