My tires were still worrying me, so I took my car to the Discount Tire and got them checked. The Wal-Mart lady was WRONG! My tires were NOT ok. There were metal threads hanging out of one of them. I bought four new tires in Provo and then drove to Moab.
I set up camp at the Slickrock Campground for 23 dollars a night. It wasn't the prettiest spot, but the national parks' campgrounds were full and I only intended to use it as a place to sleep and shower. A problem with car camping can be the noisy neighbors. At 2:30 the first night, they were up partying, drinking, and keeping everyone awake. One of them was playing the guitar and singing off key. Then they turned on their radio! Someone called the police. The cops told the guys if they had to come back, someone was going to jail. The noise died and I finally got a little sleep. The next night, they turned on the radio again. A woman went over and asked them to turn it down. A few minutes later they were arguing loudly in French, but they turned off the radio. The last night, they were gone.
Next time I will camp in a national forest and pay $3 -$5 for a shower at the commercial facilities instead. There are plenty of them in the area.