Many Tucson neighborhoods have alleys halfway between the streets, and walking down these can be productive, as they provide access to more and better vegetation than the street fronts. Look for native mesquites, blooming eucalyptus, oaks, and weedy patches. The one drawback is barking dogs, their noise preventing you from hearing the chips of warblers responding to your pishing.
You probably won't find anything rare, but you never know. I found a Chestnut-sided Warbler in someone's yard one winter – it responded to my pishing almost immediatly, nearly flying into my mouth. Alleys might be where we tally the last remaining Inca Doves in Tucson. At the very least you'll add more Yellow-rumped Warblers and Anna's Hummingbirds, and those do count by contributing to the long-term database.
Another unbirded and under-appreciated habitat is the "pine forests" of apartment complexes. I've found many Plumbeous Vireos, Cassin's Vireos, and Black-throated Gray Warblers over the years by walking into the courtyard of such well-watered apartments and pishing into the pine trees for a few seconds. If enough of these are searched, someone is bound to find something rare like a Pine Warbler or Townsend's Warbler.