OP - There are many great boondocking places along the Colorado river. For example south of Ehrenberg, AZ, a dirt road runs along the Colorado River for miles. I've not been to the end of it, but have been down 15 miles or so and there are numerous riverside campsites. Some are really trashed so take a couple trash bags and in no time your campsite will be cleaned up and ready for you.
Near Lake Havasu City many folks stay for free at Craggy Wash...
Craggy Wash Free Camping LocationA few miles further south on the California side of the river, free camping is allowed west of Earp, CA, which is just across the river from Parker, AZ, there are thousands of acres of open BLM land to camp. Many folks stay here...
Earp California Free Camping LocationsEast of Parker AZ are thousands of acres of BLM managed lands available...
Free RV Camping Near Parker, AZStill in the Parker area, stop at the CRIT (Colorado River Indian Tribes) wildlife office in Parker on the east side of town. I don't recall the office address but you should be able to figure it out with a phone call to the CRIT main office. They will sell you a short term permit to camp at one of their numerous isolated campsites along the Colorado River for cheap.
This page shows the free camping locations near Quartzsite...
Free RV Camping Near Quartzsite, AZOne more idea about cheap camping in Arizona is their state lands. For $15 individual or $20 for a family, you receive a one year permit to camp on Arizona State Trust Land. This may be one of the best deals anywhere as Arizona has vast tracts of state land. Check out the particulars here...
Arizona Land Trust PermitsThat should get you started!