Short- or long-term housesitting?
I have never done this, and have no interest in doing it myself (I love my own bed every night!) but I think there are some folks who make a "career" out of doing this.
Perhaps investigate opportunities in college towns? University listserves? Craigslist? I know my aunt and uncle who were college professors took sabbaticals every few years, for 6-9 months at a time. One of the big hassles for them was finding responsible housesitters to stay in their house for the duration. Oftentimes a visiting professor, or a graduate student, or exchange students would fill the bill. They got a free place to stay, and my relatives knew the house was occupied and looked after. The housesitters didn't have to do maintenance on the property - at the most they might have to call a pre-arranged repair service, or a local relative (yup - that would be ME!) if something needed attention.
There may be other industries in which people take sabbaticals, but I am most familiar with the academic/college environment, since my extended family is heavily weighted in that profession.
Some housesitting gigs might also include petsitting, I suppose.
Just some thoughts, since it would give you a chance to try out different locations without having to commit to a lease, etc.
Edited to add: a quick search on "housesitting in the US" turned up a "matchmaking" service for housesitters:
House Sitting Made Easy: TrustedHousesitters.com. Apparently you can join, create a profile, and be matched with housesitting opportunities.
I don't know anything about them; just providing the info as a starting point if it interests you. Good luck!