The Golden Gate is sealed into the eastern wall of the Temple Mount, facing the Mount of Olives. Its importance is out of proportion to its size: Jewish and Christian traditions both attach messianic meaning to the gate, and its blocked arches are one of the Old City's most charged pieces of stonework.
You see it from outside rather than pass through it. Come as part of a walk around the eastern walls, where the view also takes in the Muslim cemeteries and the slope down toward the Kidron Valley.