If you want pretty, stay at the Alpine Lodge in Cooke City, just outside the northeast gate. This little town is what I would dreamed a gold rush town would be 100 years ago. The lodge is very nice and clean with a young couple owning, really looked after the guests. Parking lot is gravel so be careful. Several good restaurants within walking distance.
AVOID the east gate to Yellowstone because is under construction with some seven miles of gravel road. You pray it does not rain when you ride this mess. I was there in the middle of July and made the mistate, rode it once. Never again, until it's completed.
Be sure to ride the BearTooth Highway (Hwy 212) from Cooke City to Red Lodge, Montana. Breathtaking is an understatement...
Enjoy