The next block west has Hub Ice Cream, very good.
For west side trails, Wasson Peak is a good loop. Park across the road from the Desert Museum and take the King's Canyon Trail up to the Norris Trail to the top, west on the Norris Trail to the Sendero Trail to the Gould Mine Trail back to the parking lot for a 7.5 mile loop with 1750 foot climb/drop. There are a bunch of other loops you could make.
Saguaro NP West trail map
Pima Canyon in the Catalinas is good, maybe make a key-pass loop with the Finger Rocks Trail (extremely steep).
Sabino Canyon is very pretty with a tram and lots of trails. The Seven Falls trail is very scenic. The Sabino - Bear Canyon (Seven Falls) loop is very nice but rugged.
Lots of Saguaro NP East loops start at the Douglas Springs trailhead at the east end of Speedway Blvd.
https://www.nps.gov/sagu/planyourvisit/upload/sentinel_2013_rmd.pdf
https://www.nps.gov/sagu/planyourvisit/upload/RMD-Hike-Map-2015-back.pdf
It's heating up so: Lots of water, sunscreen, a hat with brim, white cotton long sleeve shirt, cotton shorts or pants, good boots are my standard hiking attire. More water and salted nuts or other salt and electrolyte source are recommended. A white long sleeve cotton shirt will be cooler than bare arms in the Tucson sun.
Edit:
If you'd rather hike in the trees, Madera Canyon in the Santa Rita Mountains south of Tucson offers a bunch of trails.
Mexican: Little Mexico on Irvington at 12th Ave is good sitdown. El Sur on 22nd St at Craycroft is good. Raspados la Nina on Park Ave between Drexel and Bilby has the best tacos and raspados in town.
Tucson has world class roach coaches. El Nene on Flowing Wells at Wetmore is very good. Try the Yaqui Taco and the chipilones. Jason's Taqueria on 22nd between Wilmot and Craycroft also has great chipilones. El Manantial at the corner of 36th and Park has great Sonoran hotdogs and tacos.