doss1,

If this thread really has consolidated key prior threads, then there should be a great deal of info in it. So skim if you have not.

Flying in and out of SLC (or DEN for that matter) will cost you a day of drive time each direction. Consider flying into JAC, BZN, BIL, or WYS, as they are all much closer. And depending on how much a one-way charge on a rental car is, considering an open jaw or two one-way flights, maybe flying into BZN and flying out of JAC.

To make the most of your days, I would stay inside the park if feasible. And I would try to stay at least 2 nights each place so that you are not using up time every day with checking in and out, packing and unpacking. Reserve on Xanterra's website. Be aware that some rooms do not have their own bath, so you would be using a hall bath, though they are pretty clearly noted. If you can get rooms, I suggest staying in the Old Faithful area (OFI or Snow Lodge) and then one or two of the other areas, such as Lake, Canyon, Mammoth, or Tower.

NPS Day Hiking link, with which you can fill up your days: https://www.nps.gov/yell/planyourvisit/dhsampler.htm
I think the ratings on those trails that I am familiar with are fairly accurate. Have several alternatives ready, as you may find out from rangers that some trails are closed due to bear activity or other reasons.

Remember that you will be gaining significant elevation between STL and YNP, so take it easy initially and have lots of water. From prior experience, I know that Jackson and Bozeman both have Wal-Marts and other stores where you can stock up with food and water after flying in, as well as hiking poles (or broom poles if you want to go cheap), bear spray, etc.

Grand Teton National Park, just south of Yellowstone, is also quite beautiful and has several good day hiking trails. Flagg Ranch, Togwotee Lodge, or hotels in Jackson are outside the park but provide easy access to GTNP. So I would encourage you to look at that park also as part of this trip.

Seven to ten days might be a more realistic budget for seeing the two parks, so assume you won't see everything and will want to come back. These park don't work well for a lot of brief stops to check off getting to all of the key points.

Feel free to post or PM with questions. I am actually going to the park in about 2 weeks.

TRRed