Big question is whether or not you drive/have a car. Your options increase vastly if you do. Depending on how specialized your therapy needs are (?), I might start there and work backwards. Then consider what time of year/weather. There are many, many places in the US where housing is vastly cheaper than NYC, especially if you can drive.

So, for example, I live in the DC metropolitan area--not sure if that would be "far enough" from NC/NYC as it is pretty much halfway in between. But ample biking/hiking in the vicinity, and housing is quite reasonable once you get away from downtown/the inner suburbs.