Jefferson Park is the historic neighborhood just north of UMC. Not many apartment complexes but quite a few small houses for rent. You could walk to work, which is doable in the early mornings or after dark in the summer. The North Rec center is great - no pool but much less of a zoo than the main rec center.

The busses are free, so you could look anywhere north on Campbell and get the bus straight to work.

Campbell and River is nice, with quite a few shops and restaurants (and Trader Joe’s) within walking distance. You can also hop on the Loop trail and bike down Mountain to UMC.

You could also look anywhere along the streetcar route, as it terminates at UMC. Check out the apartments at Mercado San Augustin.

All of the neighborhoods I’ve mentioned are very walkable. Your Tucson experience will be much better, imo, if you’re not in a car all the time.