We went to the Black Hills at that time just this past summer. It really wasn't that bad, though we stayed in Custer, which is quite a ways south of Sturgis. Be sure to make reservations early. We stayed at Beaver Lake campground, it was very quiet at night.
2013 Starcraft Travel Star 229TB
2011 Jayco X17Z(traded in)
2010 Jayco Jay Series 1207(traded for the 17Z)
2011 Chevrolet Silverado 2500HD Z71 CC 6.0L/3.73
Reese "Pro Series" 800lb Trunnion WDH w/sway control