Zion and Bryce are 2 of my favorite places to visit from Las Vegas. If you pick either of the NP to camp, you can drive to the other in about an hour or so (each way). You can just do a day trip going to the other NP. There is a full hook up CG right by the gate of Zion NP. It is called Zion Campground. There are few spots that are back-in, and have access to the river.
https://zioncamp.com/zion-canyon-campground/
If you decide to go to Bryce, we camp outside the gate. Full Hook-Up, called Ruby's Inn RVCampground
https://www.brycecanyoncampgrounds.com/
Of course there are CG inside the parks. But mostly No Hook Up.
Have fun with your trip.