Fort Thompson is in central South Dakota, on the Crow Creek Reservation in Buffalo County. It is not served by public transport of any kind — a car is essential. The nearest town of any size is Chamberlain, about 30 miles to the south via US-16 and SD-47, which has a gas station, a few restaurants, and motel accommodation. Pierre, the state capital, is roughly 50 miles to the northwest.
From I-90 (the main east-west freeway across South Dakota), take Exit 265 at Kimball and drive north on SD-45, or Exit 248 at Chamberlain and drive north on SD-47 along the Missouri River. The SD-47 route along the river is more scenic. Flying in is not realistic — the nearest airports with regular commercial service are Pierre Regional Airport and Sioux Falls Regional Airport, both over two hours away by car.