Ask Mr. Smarty Plants

You have a couple of options for trees that would be safe next to a patio. Small understory trees under 20' would be one way to go. A few to consider would be a Ptelea trifoliata (Wafer ash), Ilex decidua (Possumhaw), or the Cercis orbiculata (California redbud). Although these trees are pretty and could offer you some shade in the summer months, they are deciduous, meaning they would lose their leaves over winter.

If you are looking for a larger tree, depending on where you are placing the tree, a Quercus emoryi (Emory oak) would maybe work. In Arizona you don't have a lot of water and the soil doesn't have much organic matter to work with. This helps keep the root system under control. As long as the spot you are looking at is a couple of feet off of the patio and not a cut out inside the patio you should be ok. If you notice, you may see Oaks along streets and sidewalks in your area. If you find a big shade tree along a street with no root damage to the sidewalk you can consider that tree a good option. It doesn't hurt to check out parks and schools in your area for ideas.

If you are really nervous about the patio and just want to play it safe, you can't go wrong with a mesquite. Prosopis glandulosa (Honey mesquite) works for your area. You might also try Prosopis glandulosa Maverick ™ which is a naturally-occurring thornless selection for Bexar County (San Antonio, TX) and should work for Arizona as well.

Prosopis glandulosa

Cercis orbiculata

Quercus emoryi