Welcome aboard Aguilar and family!
Was transplanted to Southern California many years ago, and camped just about everywhere. Although the Jeep and tent didn't have those pesky length restrictions...ha!
Have you checked out the Anza Borrego Desert State Park? It has a nice cross section of dry camping, RV Parks to RV Resorts scattered about. All depends upon your power needs.
Then there is Calico Ghost Town just outside Barstow. Our kids, and grandkids have all enjoyed this one.
And don't get too worried. Not EVERYTHING at the Colorado River needs a membership. We've vegged out at various Blythe campgrounds a couple times, just fishing and birdwatching.
Recommend you pick up the latest edition of Trailer Life RV Parks and Campgrounds Directory. It's far from perfect, but a great starting point. THEN you can triangulate with this website for real people feedback.