The time to drive to Tucson just depends where you go. I live on the far Northwest side and it takes me about 90 minutes to get to Phoenix. So if you were to go to the Desert Museum or Saguaro National Monument for example that would be another 30-45 minutes. I would give yourself 2 hours to get anywhere in Tucson from Phoenix.
Kartchner Caverns is close to Bisbee so I think that would be about a 4-5 hour drive from Phoenix. Nogales would be about 3 1/2 to 4 hours from Phoenix I think. If you are looking to do things that are close to each other I recommend this:
- Tucson Far West Side - Desert Museum, Saguaro National Monument, maybe Old Tucson (old west amusement park and working film studio - there was a huge fire years ago and unfortunately they never really rebuilt it to what it used to be. It is basically a shell of what it was when I was a kid. Also overpriced, unless really interested I recommend skipping this).
- Tucson South - San Xavier Mission (I forgot this one), Tubac, Nogales (I recommend Tubac and Nogales if you are looking for regional souvenir shopping). Youi do have to cross the border to go into Nogales, I am not sure if you need a passport or not. You didn't but that may have changed recently.
- North of Tucson, closer to Phoenix - Biosphere
- East of Tucson (and farthest away from Phoenix) - Colossal Cave, Tombstone, Kartchner Caverns, Bisbee
I can only comment on Tucson restaurants but for great mexican food I recommend El Charro (the downtown location). However, it is very hard to get bad mexican food in Tucson, just avoid the chains (like Macayos).