Have been during the big show time, have stayed in Spearfish motels about 20-30 miles West of Sturgis, or tented in and close around Sturgis, twice in Deadwood an air B&B and at a friend of a friends house.
One year I had to plan a ride for friend to Rushmore and we spent the night at the Best Western in Sturgis the week before the rally started, that was kind of interesting because some vendors already setting up and you pretty much have the entire town to wander around in without the hordes of bikers.