Deadwood is an okay location. It is the only gambling town in South Dakota. There are video games located all over the state, but Deadwood has full-fledged gambling. With 3 teens that might not be an ideal location. One good thing is that there is a go-cart/mini golf . . . place called Gultches of Fun that they may really like.
We live only 2 1/2 hours from that area of South Dakota. If I were to plan a trip, I'd probably have my home base be Rapid City. It is on the East side of the attractions that you want to see, but an easy drive to and from attractions. There are restaurants, shopping (important for teens), and motels in Rapid. You might want to stay at a couple of different places to get the feel of the area. Keystone, SD is a neat Black Hills town along with Deadwood and others.
Hope this helps! If you have any other questions, let me know. It is an area that I am pretty familiar with. Just private message me and I'll reply ASAP. Happy planning!!!