We actually did this, to a degree. Bought 20 acres in SE Missouri, near Mark Twain Forest. Virgin land, so we cleared about an acre of it. Hard work. In the end, we enjoyed full timing on it for a week or so at a time. I paid around $20k for the property -- yes, 20k. Sold it few years back for around 27k. Never had electricity, utilities of any kind. Was nice. Taxes around $70 per year. No, I didn't forget a zero.
We did not do it to the degree you want -- multiple locals around the country. But yes, thought about it.
I suggest landwatch.com -- they have tons of property from commercial to open land from lots to acres. This is where we found our 20 acre chunk...in the end though, about a year and half went by and we had not been to it. IT was fun, and if I could would do it again...desert this time?
Go for it.
