We booked 10 months in advance with a ranger from YS, he was excellent and answered so many questions I had. If you have the senior pass for National Park's, there's no admission fee, which we were.
We flew into Rapid City's airport, nice and small compared to what I am used to! Got our new car at the cheapest rate for 23 days! We stayed there for 4 days, did all the attractions that everyone mentioned. Headed to Devils Tower and stayed over night in that area. We headed to Cody for 2 days, the museum was excellent! Went to a concert at the Cody Theatre and saw the Buffalo Bill Dam. Then off to Yellowstone for 9 days, we actually stayed in different hotels in the park. I loved everything about Yellowstone, bison, bears, elk and others. While staying at Mammoth, right across from our window, a mother elk gave birth! It was amazing to say the least! I got pictures of the baby nursing.
From Yellowstone we headed to the Teton Mountain Lodge at the Teton Village for 6 nights. You can take a ride on the aerial tram or the gondola which goes up the mountain and has wonderful views. This location was a short drive to Jackson. Along the way, we always saw moose, something we didn't see at YS.
Traveling back Rapid City to fly home, we drove through the Shoshone Mountains and headed to Casper for an overnight stay. We took the long way because we had time and we wanted to really see all of Wyoming. We actually plan to go back to Wyoming within the next few years.
Have a wonderful trip!