Rock climbing at Mt. Lemmon. There are over 2000 registered climbs there, really something the locals get into. If you are a serious bicycler, there is the tour de Tucson. Or you can just ride up the mountain as high as you can and come back down. Lots of camping up there, nice trails. Fun during the winter and spring especially. Practice good wilderness safety as there are bears up there. If you want more, I'll ask my sister, she's lived there for years now. over 5 years ago
There are excellent hiking trails and rock climbing up Mt. Lemmon. Enjoyable hiking and scenery in Ventana Canyon. In fact all along the Catalina mountains.
You can even ramble off trail up those mountains. I on no did that to Esperero peaks (I think that was the name).. but we got lost and it turned into a 9 hr hike in the heat, so take a good camel bak with you LOL
There is the Tour de Tucson yearly bicycle race if you're into that. about 4 years ago