Although I just moved here, I have been going out to Mt. Lemmon 3 times a week; no less than twice. I get an awesome workout and the views are amazing. Depending on what you're into, there are plenty of trails differing in difficulty and tons of stuff to see if you go off trail.
Personally, I like to climb and explore. Scrabbling up boulders and reaching the top of the mountain is awesome strength training and the rush is amazing! There is plenty of wildlife to see (deer, mountain lions, bugs galore).
I highly recommend Bug Spring Trail. Its about 4.3 miles long. Desert-like atmosphere with differing elevation. There is no shade so be sure to bring plenty of snacks, water, and sunscreen.
Another place I frequent is the picnic area just after mile 11. It is cooler temperature-wise and is more of a forest climate. There are tons of areas to explore and even has fairly clean bathroom if you aren't as keen on watering the trees.
Hope this helps :)
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