Well, if you don’t have reservations in or near the park already, be prepared to have tp stay pretty far away to find a room. There isn’t a whole lot in the way of lodging around the park. Having said that, Yellowstone is amazingly fun and beautiful. Go onto the national park service website to download maps of the park so you can plan your trip now. I wouldn’t spend less than three days exploring the park, because it is HUGE. Give yourself enough time so you don’t miss anything awesome.
Also, one of my favorite national parks, Grand Teton is just south of Yellowstone (with the quaint, but busy, town of Jackson Hole right next door). If you are in the Yellowstone area, Grand Teton is not to miss. It is breathtaking.
If you are stopping in Cheyenne on your way there, expect at least another whole day of driving to get to Yellowstone. Its pretty easy driving on I-80 (the highest point on I-80 is right outside of Laramie (where I live), you’ll see a big sculpture of Lincoln’s head. 8600 feet). I would take 80 to Rock Springs where you’ll take 191. You’ll take that for a while, then it merges onto 189. This will take you to Yellowstone through the south, so you’ll hit up Jackson Hole and the Tetons before getting to Yellowstone. There are many other ways to go, but this is one of the easiest.
On your way home (if you’re going East), leave Yellowstone from the East entrance and you’ll pass through Cody, Greybull, then you’ll start going South to Worland. Pick up I-90 and start your journey back east. Near Sundance, you’ll be able to see Devil’s Tower from I-90, but you can always stop and take a better look. Its pretty cool.
Hope this gives you some ideas. Have a great trip.