Reaching deeply north into the South Fork and positioned between Water Mill to the west and Sagaponack to the east, Bridgehampton has a name that begs for even more geographical clarification. This one is easy: The bridge in Bridgehampton refers to a bridge built across Sagg Pond by Ezekiel Sandford in 1686. Bridgehampton is undeniably the essence of posh, and for many Hamptonites, the summer simply does not end until the occurrence of the Hamptons Classic, one of the largest outdoor horse shows in the country.