Your schedule doesn't look good for seeing much in Tucson. If you decide to drive out of Phoenix the evening of your interview then forget Mexican restaurants in Tucson as finding them at night wouldn't be much fun. I-10 through downtown Tucson is messed up right now with most of the exits closed. Also, traffic on I-10 from Phoenix to Tucson is getting stupid. You really have to pay attention as some folks are going ninety and others forty five. The stretch from the rest stop east of Phoenix through Casa Grande is a speed trap. The TTT truck stop on the way out of Tucson (Craycroft exit) is good.
If you hang out in Phoenix until the next morning then I do recommend seeing the San Xavier del Bac mission south of Tucson (I-10->I-19->5 miles south->San Xavier Rd->~1 mile west. Return to I-10 East via Valencia Rd. The current building dates to ~179, houses intact santos and frescos, and is still a functioning parish church. The place is deeply spiritual regardless of your religion.
If you go to the mission and want to try Sonoran style Mexican food then come back up I-19 to Irvington Rd. Go east on Irvington to 12th, South on 12th 0.5 miles and look for El Guero Canelo with a red-white-green awning on the east side of Irvington. If you hit Nebraska St you've gone too far. Canelos is very casual, even by Tuscon standards, and the food is good. In your previous posts you mentioned feeling a bit out of your comfort zone with all the Mexican Americans in Phoenix. In South Tucson you'll definitely be in the minority as the area has been majority Mexican/Spanish speaking since before there was a US. Canelos is worth the trip just to experience the most highly refined Spanglish in the world. Try the Mexican hotdog with everything.
Another recommendation is La Huerradura on the northeast corner of St Mary's and Grande Ave. When you come into Tucson take the last exit before the closure (Prince Rd, I think) and stay on the I-10 frontage rd to St Mary's Rd. Turn right (west) on St Mary's and drive for about a half mile to Grande Ave. La Huerradura is in a tiny salmon colored building on the NE corner. Park in the dirt lot est of the restaurant. The pozole (pork and hominy stew) is awesome and if you eat pork, I highly recommend it. If you like menudo, it is also very good.