It really depends on where you live. All the young families live in Sahuarita or Vail/Corona De Tucson. The best part of the city is north east, although not a ton of young families. Those two communities are the best for families though.
So anyways, Mt. Lemmon is 9,100 feet high, so the mountain air isn't too far away.
Sabino Canyon is awesome to hike, and really there are a ton of places to hike.
Mountain Biking is fun.
Desert Museum.
Splash pads around town.
Make sure you are near a pool.