If you're really desperate, the big hill that overlooks Sand Hollow SP has lots of camping places. Last time I was there I had it all to myself. One particularly nice spot overlooks the state park. But if you have dogs, watch out, lots of cholla.
There's a spot on the right side of the road just a little ways up Kolob Terrace Road that has a lot of space, right next to North Creek. That where I camped last time I went. It was also January 2018, so it may be a lot busier this time of year.
We found a great campsite for 2 nights off the Smithsonian Butte road where we had neighbours that we could hear occasionally, but not see. Keep in mind that camping is not allowed within 1/2 mile of the main road, and that ( 6 years ago) the road up from Rockville had a section that was moderately steep and rough. No problem in our Tacoma, however we encountered an abandoned sedan stranded off to the side on that section.
try Gooseberry Mesa or the BLM land near Virgin. There are tons of campsites.
Also Guacamole Trailhead on the backside of Zion. You'll have the view of Zion all the time