If you come in from Bozeman, there are a couple of options on how you can get to Yellowstone. You can go through Gardner, which is about an hour 1/2 drive. You go in though stone arches. Gardner is a neat little town with lost of tourist stuff there. http://www.bozemannet.com/gardiner/ is a good place to find out what is there.
Or you can go through West Yellowstone, which again is about an hour-/12 drive. It is a forested drive with a good chance to see wild life. http://www.westyellowstonechamber.com/ is a good way to find out what is there.
If you come in from Billings you well enter through the Cook City High way. It is a little over an hour to Red Lodge and then you start one of the most spectacular - breath taking highways anywhere! Although if you are afraid of heights, I do not recommend this drive! It is a little over an hour's drive to Cook City on slow switch back high way. (I always found the movie Horse Whisper funny, because in the drive out here they stop at the battle field over by Harden and then the next shot is of them going over this highway. Only thing is, they run parallel to each other and they would not take both highways. LOL) The Alpine Hotel in Cook City is a nice place. My brothers use it year after year when they go snowmobiling up there. http://www.allredlodge.com/cooke_city/ is a good place to see what is there.
If you are a senor, you can get special rates for getting into the park. It does cut a fair amount off the cost, as they often charge by the vehicle. And once you get this fair, you can then use it to enter any of the parks. I think my mother has one she purchased so she never has to pay to get into any of the parks again.
Favorite thing: My car has spent its entire existence in the blazing heat of Arizona. On our last night at Yellowstone (June 6), it snowed and froze. The car battery was unable to cope. I got a jump start from the service station at Canyon Village but it did not have a replacement so I had to drive over the mountains to Cody without turning off the engine. Trying to find a battery in Cody for a Toyota looked like Mission Impossible until we found the Technical Cowboy, whose shop is a block north of the main drag and highway. He had a new battery in stock, installed it and had us back on the road in 15 minutes. His price was extremely competitive, too. If you have car trouble in northern Wyoming, I highly recommend the Technical Cowboy in Cody.
In 1872, President Ulysses S. Grant signed a law declaring that Yellowstone would forever be "dedicated and set apart as a public park or pleasuring ground for the benefit and enjoyment of the people."
For many years, I've read about this wonderful park and always wanted to visit...so after passing the turnoff on my many trips to Canada, I decided to take the plunge and visit. Words can't begin to explain the sights and sounds that you see while driving through the park, but before you leave this planet, you should make a point to visit Yellowstone.