The Devil's Tower Trading Post is a Huge souvenier shop just outside the entrance to the park. They have every imaginable item with the Devil's tower name or image emblazoned upon it. The best thing about the shop though is the view from the Parking lot. They have THE perfect promotional shot with the store in front and the tower situated right behind it.
Open April 1 thru November 30 - 7am to 10pm
What to buy: The best thing I got here was an insulated Devil's tower bag. It kept our bottled water cold and was great for bringing all of the rest of our goodies from the remainder of our trip.
They also have a lot of "close encounters of the 3rd kind" sort of stuff. Not my thing, but I'm sure there are tons of people who eat that stuff up...
There are several souvenir shops near the base of the monument, including items featuring Mt Rushmore and the Sturgis motorcycle rally.
What to buy: Buy a coffee mug or a magnet of your destination. Stick with useful things that won't just take up space but will return their cost in some particular way.