Renting a house or a cabin would be a great idea, and there are a lot of choices for rentals in the PA area. It s best to do your homework and use online research to find available places to stay that fit within your budget.Rather than give you a specific property name and location, I would suggest that you do some research on the available houses/condos, the prices and the locations. I have used justvr.com for vacation rentals in the past and it was quite helpful for narrowing down my choices and booking a few nights stay.
The Poconos have slowly become exurbs of New York City, so many of the natural things of the past are long gone.However, there are still a few places west of the touristy areas where you can still rent cabins. Try Split Rock although there are a few others near Lake Harmony.