I guess we live here so we may take some things for granted, however if you are planning to be in the hills, the Mammoth Site in Hot Springs is pretty good. If you are in Deadwood, they have a lot of Crab Leg and Prime Rib Buffets, the one in the 2nd floor of the Gold Dust is the best otherwise the Deadwood social club is good as well, it's up a staircase right by Saloon #10. Rapid City has Sanfords which makes great and unique sandwiches and has lots of beers on tap to choose from for dining option. Many people really enjoy the prairie dogs so stop and see a prairie dog town. I know there is a commercialized one on I90 near Wall, however you can probably find one of these in Custer park arounds the roads as well.
We live in Pierre and there generally is a nice walleye bite here in Sept if that's your thing. Or Salmon up by Whitlock Bay near Gettysburg that time of year. If you are near Gettysburg, Whitlock Bay Supper Club serves what is in my opinion some of the best prime rib anywhere on Saturday nights, otherwise Bob's Resort a mile away from this serves great sirloin steaks with a great view of the river. Unless you are a huge eater, the steak sandwich is probably big enough as it is about 18 oz. You can get bigger. You will be here in the beginning of preserve pheasant hunting season, if you've never pheasant hunted in SD you are missing out.
Wall Drug is a real tourist trap with not much to see in my opinion time is better spent in the badlands. Mitchell has the corn palace where they decorate the outside with different scenes each year and it's all done in colored corn. Not a lot to see inside but definately worth a drive by. The rest stop on I90 by Chamberlain has a decent Lewis and Clark display with a great view of the river. It's not a destination, but a nice stop as you are driving right by and I think it's free. If you are driving by Vivian stop at the Junction for a peice of pie they are known locally for great pies. Sioux Falls has the Sertoma Butterfly Gardens, and Falls Park. If you like gardens and such, Brookings has McCrory Gardens that SDSU manages that is good as well. The Ram Pub has decent prime rib or sandwiches or Cubbys Sports Bar has great foor as well in Brookings.
The rally is over today in Sturgis so the main hooplah will be gone by the time you get there and aside from the motorcycle museum, this really is just a normal small town. Devil's Tower in Wyoming is an option in that area as well. If you have anyother questions let me know I'd be happy to help. Enjoy your vacation.