That's how we did it-compliments of United miles! Those airfares are really expensive! We stayed 5 nites-3 in Grand Tetons, 1 in Yellowstone, and 1 in Jackson Hole. Each nite we were in a different hotel/cabin-
Colter Bay was VERY plain/rustic
Flagg ranch-we paid for a view cabin and LOVED it. The coffee maker in the room was a real plus when we got up at 6 am to see wildlife
Old Faithful Inn-our only night in a hotel, rather than a cabin, and I think being in a national park, we missed the cabin experience. Also our room was way down on the 1st floor of the west wing, not too desirable. I don't even have a picture, but if you've seen WL, you kind of know what OF Inn looks like.
Jackson Lake Lodge-absolutely beautiful. Probably the most scenic resort of our trip. We sat on the benches outside the main lobby for hours. And it was fun that a ranger was there in the early morning with a scope to help see things. And the coffee maker again!
In Jackson, we stayed at Cowboy Village, great little cabins with a 2 burner stove, refrigerator, and once again-the coffee maker. Sort of like Fort Wilderness-
Sorry this is so long, but I remember before our trip, where to stay was foremost on my mind. Feel free to PM me if you have more questions.