Does anyone "nomad" in the United States? What are some good cities?

Like many of you, I have a flexible, work-from-home job, so I can work anywhere there’s an Internet connection. I’d like to see more of the U.S. and maybe live somewhere for 2-4 weeks and experience it in more depth than a regular vacation, and actually work while I’m there. Does anyone have any experience with this? Tips for low-cost cities? Ways to stay in some place for approximately the cost of rent?