A very slightly different way to say stamping ground is stomping ground. Either way, you're talking about a place you love to visit, a usual hangout, or even the neighborhood where you live. You could say, for example, "In college, Harvard Square was my regular stamping ground." The phrase, which came into use in the 1820's, comes from the way wild animals sometimes mark their usual territory by stamping down the soil or grass with their paws.