Looking for a cabin for a week?

I'm willing to go anywhere in the continental US to find a cabin in the woods or the mountains where I can spend about a week - probably including the Memorial Day weekend. Many state parks have reservable cabins like this, but I'm looking for some experienced advice. I would be alone, so it doesn't have to be big. Probably the main restriction is that many of these places are already reserved for the period I want (roughly May 21 - 28, although there is some flexibility). It doesn't have to have a phone or a TV, but I want to be able to shower and cook, and I would at least want electricity. I'd like stay under $100 per night, but that's not an absolute requirement. But I don't want a beach or lakeshore cottage - I want it to be shaded, preferably deeply.

Any ideas?