Onion Creek
There are two Onion Creek camping areas. Upper Onion Creek is the most popular and has several group sites. The Lower Onion Creek site is a 1/2 mile further down 128 (going east). It is very secluded, I have never had a problem camping here even though it is for groups. There is a pit toilet on site. Camping without reservations is $2.50 per person per night. A calendar that shows availability is posted closer to the site, not on the kiosk. If no one is on the calendar you are free to camp (but you must pay). Often there is no envelope here to deposit your money and tag your site. Be sure to stop at one of the other camping areas along the Colorado River to pick one up. This is a remote location with a great sunrise looking at Castleton Tower to the west and Fisher Tower just behind the site. There are fire pits and you must bring your own firewood. There are also picnic tables.
Even though this is 20 miles east of Moab, I prefer Onion Creek over the other closer sites especially if you want quiet!