The two major cities in this area are Cedar City and St. George. I live 45 miles south of Cedar, and about 18 miles east of St. George at the "gateway" to Zion National Park and the Grand Canyon.
There are places to stay in St. George of course, and a lot in the way of places to eat, etc. But there is also the city traffic and atmosphere. For many of you that's not a problem, but I prefer the small town atmosphere so will recommend staying on the east side of the county.
There are 3 state park campgrounds east of St. George. Red Cliffs campground is just 16 miles up I-15 to the northeast. It is accessed via the frontage road south of Leeds. Quail Creek Reservoir and campground can also be accessed from the same frontage road, or from SR9 on the way to Hurricane. Sand Hollow Reservoir and campground is just a few miles south of SR9 on the west end of Hurricane. If you are self contained, there are a lot of places on BLM land where you can camp up to 14 days without paying a fee.
I'll try to post up a map later on with camping places detailed.