The Menlo T. Hodgkiss Memorial Gymnasium (or "Hodgkiss Gym") was an athletic facility on the campus of the University of Mississippi in Oxford, Mississippi on Earth. In 2245, it was the site of an interplanetary gymnastics competition judged by Emony Dax, among others. (DS9 short story: "Old Souls")

There does not appear to be a Hodgkiss Gym on the present-day campus of Ole Miss. It is described in the story as a relatively new building, though on a 400-year-old campus, it's impossible to speculate how old "relatively new" might be.