Hello,
We live in the black hills of South Dakota, we are in the Rapid City area! We have lived here for 4 years this Aug., so I should be able to help you with any questions you might have( just ask away and I will do my best to help you)!
What month were you going to be coming? The reason why I ask is that there is different things going out thru out the summer months.
I have never done panning for gold, so I won't be much help on that. But if you do a google search you should be able to find some good ones.
Another really fun place to check out is Bear Country( which is on the way to Mt. Rushmore)! You drive your car thru where all the bears are walking around and there is a place at the end where you park your car and can walk around & see some more bears( that's were you would see some baby bears, that they would have).
There is also Reptile Gardens, if you like snakes and such!

I have never been there myself as I hate snakes and you could not pay me to go into that place! LOL
How old are your kids? As they might like Storybook Island, which is in Rapid City. It's a cute little play park, with different classic story book characters and they do have a few Disney characters.
In Rapid City, we do have a bunch of good places to eat. We have an Applebees, Olive Garden, I-Hop, Buffalo wings( it's new), we have a good Mexican place too( I just can't think of the name right now), Pizza Hut, etc.