There is no reason to go to SLC and then north. I like I-80 past Cheyenne to Rawlins/287 NW to Lander. There is a inexpensive city park there and it's worth the short trip in the toad to Sinks Canyon SP which has a very nice small visitor center. 287 was recently rebuilt and it's one of the prettiest ways to the Tetons and then north to Yellowstone. There are two Colter Bay CGs, one with FHU. Use the toad to get around and the visitor center in Jackson is good and just inside the south entrance is the Episcopal Church of the Transfiguration which is worth a visit.
I like
Allstays for finding CGs.