I just got some travel brochures last week for Wyoming - hope to go next summer. I'd love to hear any tips you have about what to do and where to go. I also got brochurse for Montana - but after your pictures, I think Wyoming is at the top of the list.
West coast distances are much greater than what you expect on the east coast. Yellowstone is 2.2 million acres, and in parts of 3 states. The speed limit in the park is 45. Toss in abundant wildlife on the roads and tourists that stop for every squirrel and hawk and you have the makings of a slow ride. There are few roads in the park and it's more or less a figure 8 layout.
Plan plenty of time to see things. Yellowstone is so close to the Tetons it would be a shame to see 1 and not the other. Both provide amazing scenery. The Tetons you can enjoy from afar, not so much in Yellowstone where you will have to park to see some of the sites.
Finding a place to stay can be dicey. Most of the park is booked more than a year in advance. It's really too far to drive in every day from a border city but it is doable. The commute will cut into your sightseeing time.
If you go off the beaten path, carry bear spray. Better safe than sorry. Stay on the trails, they lost a young gal that got off the trail and took a header into 1 of the gorges.
Bring a decent camera, plenty of memory and extra batteries.
Let me know if you need any specific info.