Are you guys going to be staying in a hotel or are you camping?
Here is a link to DogFriendly - for the Mount Rushmore / Rapid City area.
http://www.dogfriendly.com/server/tr...ck_Hills.shtml
Also, this one looks really nice and it's only $20 per night!
http://www.safehavenpetresort.com/Overnight_suites.html