Not worth the money: Evans Plunge, Mammoth Dig, Bear Country. The main known waterfalls in the Hills can be viewed, but you can no longer walk up to them. Black Elk Peak (formerly Harney Peak) would be too hard for little kids. If you liked hiking, though, maybe you would like Mickelson Trail. The entrance is at Deadwood. It has a fee.
Windcave is reasonably priced and very good. Get tickets very early and plan wisely for your time between purchase & departure as they don't wait long. Kids should have sweaters or the like and real shoes. There are short hikes (better for younger kids) and long ones in the cave.
You will most likely see bison & prairie dogs nearby. Don't approach either. By Custer, we saw a marmot by the road. There are rattlesnakes in the Hills and surrounding areas, so just be aware. Hot Springs has some areas with black widow spiders. You will most likely not encounter these, though. Hot Springs has been dying out. Too bad, it used to have interesting shops.
Jewel Cave is good too, although more expensive. The other (privately owned) caves are not as well maintained.
Mt. Moriah Cemetery (Deadwood) is interesting, although maybe not for young kids. Keystone has a western photography place that has talented photographers. They display many on their windows.
Spearfish Canyon is very beautiful, but recently had a bunch of tree fall damage along the way due to a bad storm there this spring. The driving is slow and winding. Young kids most likely would get bored. Roughlock Falls & Bridal Veil Falls are along here.
Reptile Gardens also has my vote.
If you go on Needles Highway and Iron Mountain Road, it is slow going due to switchbacks, dropoffs and a narrow road. Give yourself at least 3-4 hours to go through. There is a small natural bridge down Iron Mountain road. Be sure to stop there and get a family picture. The drive is very beautiful. Sylvan Lake is beautiful too.
As far as drives, the Wildlife Loop is slow & long and you rarely see anything along it. You are best off using your time elsewhere.
Wall Drug is at Wall, by the Badlands, an hour east of Rapid City. Very touristy, but can be fun.
Cosmos is an illusion, of course, and can be fascinating to kids. It is pricey.
Thunder Mountain has gold mine tours & gold panning. They offer a coupon discount online. I don't know if it would be worth it, but could be fun with kids. Battle Creek still has bits of gold in it, so some say.
Sturgis is dull when the Rally isn't on, not much to see. I wouldn't take kids while it is going either, though.
The 1880 Town could be fun with kids. Four Mile Old West Town by Custer could be too. It can help spark imagination & an interest in history. Speaking of history, we liked the Days of '76 museum in Deadwood. Adams house was not worthwhile. I am not sure how the museum is, but is hopefully better.
Custer Monument is privately owned. It has a big museum and a great restaurant. Portions are large. If you go there, get an Indian Taco. They are great!
Get a vacation guide if you have time & sign up for their email newsletter. You can also check out WAY more here. This site has a lot:
http://www.blackhillsbadlands.com/visit http://www.blackhillsbadlands.com/suggested-itineraries/ten-favorite-free-things-do-black-hills-or-very-nearly-free-anyways
In North Dakota, you can stop at the Lewis & Clark Museum, or go through their badlands & Theodore Roosevelt Park. Rattlesnakes are plentiful there. Other than that, and the geographical center of North America, there is not much to see.
If you slip on over into northern WY, Sundance and a few other small places have things to offer.
Have fun!