I looked into Idaho Falls and the Swan Valley area. At the time homes were inexpensive and the game is rite out your door step and the river runs rite through the valley.
The hunting and fishing here in Idaho is very diverse, so what do you like best, mule deer, whitetails, elk, upland birds, waterfowl, trout in rivers, lakes, steelhead??
If yer wanting to get away from people, I'd pick Salmon. It has great fishing, hunting, mountains all around and not too far from larger cities in Mt and Idaho if need be...