Yes, there is a really nice spot. It's very big and white.
You can camp anywhere on the road that leads off of the freeway at the Bonneville Salt Flats exit. They clear the salt every night, so don't plan on camping there, but if you want to just pull over and camp for the night, break camp in the morning and go to the spectator/parking area it is very close. If you are in a RTT, and plan well, you could break camp and drive to the parking area in about 10 minutes.
You will see campgrounds of various ilk on your way out to the flats. Any of the land is fair game to camp on, and no one will charge you a fee or give you a bad time. Be prepared for wind at night.