Big Sky is in Montana.
Big Sky was a ranch in up until the early 1970's when Chet Huntley decided to turn it into a ski hill and resort area. It has grown considerably in the last 10 years but still is relatively uncrowded as most of the lodging in the area is houses and condos that are used infrequently.
You can fly into Bozeman and take a 45 minute drive down the canyon along the Gallatin River. There is a taxi service called KARST Stage that will take you down to Big Sky for about $60.00.
Big Sky is divided between the Mountain Village (at the base of the Big Sky Ski Resort) and the Meadow Village (that is a 10 minute car ride and several thousand vertical feet below the Mountain). Big Sky is too spread out and too vertical to really sample without a car. There is a rudimentary shuttle system that operates during busy times but not often enough too be relied upon. Taxis are sometimes available but a ride from Mountain to Meadow runs about $40.00.