There are lots of free or nearly free dry-camp locations in the southwest and other parts of the US on Bureau of Land Management or BLM property.
Most BLM locations allow free wilderness camping. You can camp for up to 14 days, within a 28 consecutive day period, then you must at least 25 miles to another location to restart your free camping cycle.
There are also a number of long-term BLM locations such as the La Posa Long Term Visitor Area (LTVA) near Quartzsite, AZ. Here, you can purchase an LTVA long-term permit ($180) that allows camping in their Bureau of Land Management campsite continuously from September 15th to April 15th (a total of 7 months), or for any length of time between those two dates.