Capital Reef is free BC permit.
Bryce is five dollars for BC how ever long your stay is.
I do believe MT Zion was Five bucks
Buy a annual pass $80 to get inside.
Navajo Nation permit is five dollars per night, but you can camp anywhere.
Cameron AZ and Window Rock AZ look for the parks department, or allow for a month to get your permit.
I am more into the dispersed camping I don't really care if costs me money. Yet can't beat free.

I spent 74 days out of 82 days doing dispersed camping last summer. Going from Phoenix to Denver via Utah, Wyoming. Turns out most of the route had a legal camping every thirty miles. I even found dispersed camping outside Vail CO. Ask the Forrest ranger at the station they will tell you all the great spots.
BLM is the hardest to find, there most likely will be no signs at all. Use a gazette map to find public space. Most libraries have them take a picture with your camera. I think the west coast is much better for this than the east.
Can you say Red Hill pass in CO. Only one road socked in with private land. The ranger lady guided me to what side of the road it was on as you couldn't see the road from a map only a blotch of land. Yet BLM land is tricky. Which I then found the sign "Please close the gate we have cows here."

Great POST.
Dixie National Forest outside Hurricane Utah. Would travel some 200 miles and still find myself choosing this forrest.