We have been to Yellowstone three times and I believe that everyone should see it at least once. I would suggest trying to stay around Cody or between there and the Parks east entrance. The scenery going in that way is tremoundous and it brings you right along Yellowstone Lake. Then you can go up to Canyon and take in the both the upper and lower falls of the Yellowstone River and Artist Point and all the other things around there. You should go up through the Lamar Valley in the early evening and make sure to take good binoculars and a spotting scope if you can get one and a camera. The last time we were there there were maybe 3 to 4,000 buffalo along the river and then they all decided to move back up into the hills on the other side of the road almost all at the same time. It was a buffalo jam with huge bulls walking along side of the car or right in front of us and it took a hour to go a couple of miles. The spotting scope is for locating the wolf pack in the hills there. When we were there last summer we were able to see 3 wolves, a black one, a silver one, and a white one that all ran down into the river bottom willows. There will be different groups of wolf watchers parked along the road and often there are Park Rangers watching and giving talks about the wolf repopulation in the Park.
There are so many things to see there with the guiser basins and Old Faithful the rivers and falls and elk and bufallo and moose and sheep and bears. There are hiking trails if you are so inclined, and if you are a fly fisherman take some gear along because you will just kick yourself if you don't. If you go upto Gardner, the north entrance, go to Parks Fly Shop and if you want you can book a guided fishing trip in the Park or a float trip on the Yellowstone River. If you trout fish there are so many rivers in this area it is hard to choose one. West Yellow is the western gate and is pretty much a tourist area with several big name fly shops, novelty shope and the Bear and Wolf Intitute (very much worth visting and watching the bears).
Back to Cody, I suggested this because there is soo much to do there. The Bill Cody musem is a must do if you have any interest in fire arms and history and Plains Indians. I think they have at least one of almost every gun ever made. I mean every thing from flint locks to Peace makers to Browning machine guns to M16s to Purdy shotguns and every thing in between. Lots of stuff on Wild Bill Cody and his life and Wild West Show. Many of the guns we saw in John Wayne movies over the years. Be prepared , it will take most of a whole day to go through every thing there. Then if you aren't too tired there is a Rodeo every night during the summer, and this is the real stuff.
On either the way out or going home you can make a small side trip to The little Big horn battle site and maybe to Mt Rushmore or Crazy horse monument. Man the more I talk about it the more I wish I were going back again, so I will stop now. Go and have a great time but again prepare your self, lodging where ever you stay will cost $250 to $350 a night unless you are adventuresome and would enjoy camping.
