Canyon Grape (Vitis arizonica) vines can be found growing in the foothill canyons around Tucson, such as in Sabino Canyon and Molino Canyon.
The fruit, young tendrils, and leaves of this native vine are all edible. The small, delightfully tart grapes can be eaten raw (watch out for the seeds) or used to make jelly, juice, or wine. The young tendrils can be eaten raw or cooked. Canyon Grape leaves can be used to wrap around other foods for baking, as called for in traditional Mediterranean recipes.
Canyon Grapes are very popular with birds, and I've had the best luck finding ripe purple grapes in higher elevation areas without numerous fruit fiends, also known as Curve-billed Thrashers (Toxostoma curvirostre), which are most common at lower elevations around Tucson.
These clever, sharp-eyed birds adore grapes, and will not only eat all the ripe Canyon Grapes they can find, they will also voraciously devour cultivated grapes, tomatoes, and a wide variety of other fruits. Voracious Curve-billed Thrashers are one of the main reasons that many Tucson gardeners have to wrap their fruit and vegetable gardens in bird netting or aviary wire.