Where is an arthroscopy usually done? at a hospital?

Surgical center: This is most often done at an ambulatory/outpatient surgical center....

Often, yes: Arthroscopic surgery is typically performed in an operating room; often these are part of a hospital, or, because most arthroscopies are outpatient procedures (ie you go home the same day), they are frequently done at surgery centers. In the past some physicians performed diagnostic scopes in the office but this is extremely uncommon. Best to do it at a site that does a lot of arthroscopies.