Given that we are coming out of a recession (at least so it appears), it is hard to guess without searching. Through the National Park Service website, you can reach the Yellowstone and GTeton sections, and from there the park accommodations website. Bookmark it even if price or availability is not there, and return every several days to check for new openings. I have no idea about camping; in a rational world which is in a downturn, I might expect more people to be camping than in a normal year. If no availability in the parks which works for timing and budget, try places in West Yellowstone or Dornan's (spelling?) or Togwotee Lodge, both near Grand Teton. In Cody, I had a good experience in a B&B in a former church several years ago; while I can also recommend the museum, Cody may be a bit out of your way, depending on your plans.