If you are visiting Yellowstone, this is one of the ideal places to spend the night, and Alpine motel was excellent for us. It was clean, and convenient. I would stay again.
Coming to Cooke City in the evening and going back to the park in the morning may seem like a long drive, but you get to do the Lamar valley sightseeing twice, at different times of the day. It's worth it. Cooke city is very cute, just make sure you arrive before 8:30 pm, most places are closed for dinner after that. Breakfast options are pretty good.