I've never been to Quartzite but can tell you that there are many many people who spend lots of time there for free. Seems your problem was arriving at a bad time, and not taking time to scout out the area before hand.
There is a site/group called "cheaprvliving.com", and also a yahoo group called "vandwellers" who have tons of experience and info on free/cheap places to stay. Go to those sites and ask for advice.
Also if you are 62 or over, you can get a lifetime pass at any National Park or Forest Service office (for $20 I believe) that will allow you to stay for 1/2 price at any Federal facility, and no entrance fees. Lots of Forest Service sites will cost you $5-$6/night with that pass. All the Forest Service sites will have at a minimum vault toilets, and most of them have drinking water.