Rolling Skies, Mesas, and Rivers.
Plenty of campgrounds to choose from, some that need high clearance vehicles, but plenty that don't and that still offer great views. I came here for an overnight bike-pack trip and the base camp I stayed at had a picnic table, fire pit, and a nice cliff with the river running just behind it. There are also restrooms close by.
Back-country dispersed camping was everything you'd expect. No amenities and camping under the stars.
Be prepared for extreme heat, cold (at night), and unpredictable weather. I had all of this.
If you forget any gear there is a small town just outside of the park where you should be able to find whatever you need and also get your tourist needs in.
Month of VisitApril