Agua Caliente Park
Agua Caliente Park is located on the far east side of Tucson near the Catalina Mountains. The park features a rare spring that rises from the ground, creating a beautiful environment fit for an afternoon picnic. Picnic tables as well as benches are available if you wish to skip the blanket. Agua Caliente Park is a great place for a quiet, calming date-style picnic.
http://www.pima.gov/nrpr/parks/agua_caliente.

Reid Park
Reid Park is Tucson’s most centrally located park, and perhaps its most popular. The park includes a large lake and small pond area where guests can set up a blanket and picnic near the water. There is no covered structure near the lake area, but plenty of trees to sit under. Take the kids by the playground on your way out or stop by the Reid Park Zoo for some added fun.
http://cms3.tucsonaz.gov/parksandrec/specialplaces.