You cannot get to South Dakota by passenger train (Amtrak). The closest you can get is North Dakota, and the distance is still far enough that you would have to rent a car and drive several hours to Rapid City.
If you cannot drive or fly, your other options would be to use Greyhound or check into tour companies.Edited: 08 July 2013, 21:58
The closest station would be Williston. Next would be Minot. However, there are a couple of things you should check into. First, I believe the train stops in the middle of the night, but I am not 100 percent sure. I know it stops in Fargo,ND at one something in the morning as I have had friends traveling westbound get on there. If I am correct about the night stop, I doubt you want to get off the train and start driving through isolated terrain in the middle of the night. The other thing to consider is the situation with the oil boom in western ND. Hotels in some towns have become places of residence for the oil workers and lodging is hard to come by. Crime is also up in these areas, although I haven't heard about anything horrid happening to tourists. I would go onto the ND forum and ask about both the Minot and Williston stops to see if lodging with the oil boom is going to be an issue and whether or not Minot would be better. I am not sure how far east things are affected. They may also know the timetable for the westbound stops. Someone else may come on here with more info, too. Good luck with you research and I hope you are able to find something that works for you.
I did some more checking and Williston is definitely part of the oil boom area and women are getting a lot of unwanted attention there. I would look into Minot, but again, ask the ND folks.
Your email was very interesting and I shall certainly take it into consideration.
Thank you for the information.
Rather than North Dakota, my college age daughter has ridden the bus from Minneapolis MN to Rapid City many times. It's about a 12 hour trip, the bus station in Rapid City is downtown on 6th St. between Main St & Omaha St.
By car, if you would rent in Minneapolis, it is 9-10 hours, your route could be interstate through MN & SD.
Many thanks - I was wondering how long it would take to drive. Much appreciated!