There's a very shady spot near the northwest corner of the University of Arizona Campus. It's a tree-covered parklet in front of the Moroney Theatre, between the U of A Museum of Art, Fred Fox School of Music, and the Center for Creative Photography. You'll find benches and very tall chairs (like this one) to sit on, as well as sculpture.
Location: Southeast of the corner of Park and Speedway. From north side of Speedway, walk through the Olive Underpass; the parklet is on your right near the south side.
Parking: The Park Avenue garage is at the north end of the Olive Underpass. All parking in the area is controlled by the University.
Hours: Probably 24 hours, though UA Police may be suspicious if you're there at 3 am…