We wanted to show my parents the desert and my dad wanted to see the Superstition Mountains, so we decided to pick a patch of desert that was on the way there. We went to the edge of Mesa heading toward the Superstitions. 
It was coincidentally the hottest day of the year so far, which of course, being Arizona in June, was pretty hot with a high of 116. The a/c in the Dodge was as excellent as ever and we brought a very large amount of water, so it was fine. Usury Mountains Park turned out to be a great place to see the desert. It was right where the mountains and the city meet and had nice paths and a lovely, air conditioned welcome center.
We learned from the man in the shop that Mesa and up into the mountains is a wetter part of the Sonoran desert, whereas Phoenix proper is drier, so Papago Park, another go to location for showing people the desert, is a drier representation.
Here is a video of the park:
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