I stopped off at the Paria Contact Station for the walk-in permit lottery to hike The Wave. Here's a google map centered on it. Here's a few photos of the station.
There were only 24 groups on that day. The previous day had 49. They post the count on the window.
Here's a video showing one number being pulled from the lot.
I did not win a permit. It was worth the short drive from Zion NP. Plus, I got to drive another 4wd route on my return. This time I drove a few miles down House Rock Road and then turned west on Five Mile Mountain Road. It was very scenic.
This road is maintained and I never had to raise the suspension. On a previous trip I took the road to the south (Route 721). That was very rugged in places.
I also stopped off to inspect a purported BLM primitive camping area along the Kitchen Corral Wash. Here's a google map centered on it. Not very appealing, except it did offer shelter from the wind on 3 sides.
I found a much nicer place for backcountry camping on BLM lands, closer to Zion NP. Here's a google map centered on it. It's easy to get to, and it's at over 5,000 feet elevation so the temperatures would be cooler in the summer months.