Hi there! I also live in South Dakota -- 7 hours away from the Black Hills, but I spent lots of time there as a child. My grandparents had a cabin in Spearfish Canyon, which is between Lead and Deadwood, so I am partial to that part of the hills.

We usually spent 2-3 weeks there every summer.
The recommendations from other posters have been great, here are more that I would add:
If you prefer a more rustic stay, I would suggest:
http://www.rimrocklodge.com
We stayed in the Ponderosa cabin a few years ago and it was a great base camp. We had family in some of the other cabins, but our cabin seemed to be the place most gravitated to as we had the kitchen -- or truly more of a "kitchenette". Rim Rock is near Bridal Veil falls and a great area to explore by foot.
Deadwood has changed through the years. When I was a kid it was all about the Wild West. Calamity Jane and Wild Bill Hickok. The saloon where WBH was shot, Mt. Moriah cemetary where they are buried etc. Did you also know there once was a Chinatown in Deadwood? It's true! Lots of rich history, etc. Some of that is still there, but it has turned into a mecca of gambling now too. Just something to be aware of with your children.
Rapid City is a small city with all the trappings of chain restaurants, hotels, etc. Great if that is what you are looking for. Mt. Rushmore is as fabulous as ever, even more so, really.
The alpine slides in Keystone are really fun, as is the Black Hills Maze not too far from there. There is also a waterpark in that area.
http://www.rushmorealpineslide.com/
http://www.blackhillsmaze.com/
http://www.rushmorewaterslide.com/
In the southern hills (less than an hour from Mt. Rushmore), we've always enjoyed:
(In Hot Springs)....
If your kids are into dinosaurs --
http://www.mammothsite.com/
For naturally warm water swimming .... (yes, really) --http://www.evansplunge.com/
Also, in Hill City, there is the Black Hlls Museum of Natural History, which includes a great dinosaur exhibit .... dinosaurs found in SD....
http://www.bhmnh.org/
And, near Custer ....
http://www.flintstonesbedrockcity.com/index.html (a bit hokey, but very charming!)
Be aware that some places are only open seasonally. Did I read that you are going in October? That may not be the best time to go if you want to have the full Black Hills experience ... sorry to say. Black Hills is more of a Memorial Day to Labor Day vacation destination.
Weather -- summers - warm during the day/cooler in evening/occasional evening showers.
Also, if you are arriving via I-90 from the east, be sure to stop in Chamberlain (just over the Missouri River bridge) as Al's Oasis for dinner. They serve buffalo burgers, have a nice salad bar and lots of other good food.
Also, as others have noted, a SD vacation is incomplete without a stop at Wall Drug in Wall, SD.
I'm sure there are lots of other great places to go to as well, but this mostly covers all of our traditional family favorites.
Have fun planning and visiting! When I was really little, I thought that every state had these treasures .... imagine my surprise to find out they didn't!
