That would depend on your interests, but the differences are, Gardiner is a busier "tourist town", which offers more in the way of lodging, shopping, and "dinning", but it's nearly an hour drive from Gardiner over to Lamar Valley, on good roads, and without stopping.
As wolfers and wildlife photographers, we spend the majority of our time in Lamar and the northeastern side of the park, and we stay in Cooke City. That area is pretty basic, and it's probably not for everyone. It's a small, quirky, mountain, former minning town that has given in very little to modern life. They have electricity, telephones, indoor plumbing, two gas stations, four or five motels/cabins, four places to eat(when they feel like opening) and even satellite TV, and a very well stocked trading post(gift shop) but no real grocery store. With the exception of the fairly new Super 8 motel and the privately owned Alpine Motel, most of the lodging is more like "camping with walls". It's clean and safe, but basic. For those of us who stay there, the draw is the proximity to Lamar, and we aren't really in the rooms all that much anyway.
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