We love Tucson.
Pima Air & Space Museum
Sonoran Desert Museum ( so awesome)
Kitt Peak National Optical Astronomy Observatory (Tucson and nearby can be so amazing at night, as there are regulations about city lighting. Great place to see the stars, even from inside the city limit)
Catalina State Park
Sabino Canyon
Mission San Xavier Del Bac
Tucson Mountain Park
Tucson Botanical Gardens
Tucson Museum of Art (proud to say DH has had things on display there)
LOTS of hiking, outdoor activities. Tucson is located directly in the middle of four mountain ranges, so it's very beautiful.
University of AZ is there.....so there are several museums on campus.
We lived in Tucson, and really enjoyed it there. You can drive not too far to really interesting places as well.....
Like:
Tombstone (cheesy, but fun), about 1/2 hour drive from Tucson. Fun if you like "old west" stuff.
Kartchner Caverns (a huge new cave unveiled only about 8 years ago, super awesome for all ages. not quite a 1/2 hour drive). near Benson/Sierra Vista.
The Shady Del. Not sure what kind of things your family likes, but this suits our family well. You can rent vintage trailers (all decked out in the appropriate time period) and stay! This is quite a drive south, not to far from the border in Bisbee, AZ.
Welcome to the Shady Dell! It's about just hanging out and enjoying each other's company. It's a beautiful area as well.
Queen Mine underground tour, also in Bisbee, AZ
If you do the Phoenix/Scottsdale thing, I recommend SMOCA (Scottsdale Museum of Contemporary Art). Also, you can visit a Frank Lloyd Wright house, Taliesin West.
I lived/worked in Tucson, but also worked in Phoenix and all of southern AZ.