Before the mid-8th century, the only gates which are both mentioned and located are in Amaziah’s wall in the Temple Mount complex (which did not extend to the City of David, contra the image in the biblical account). According to this account, the distance from the Corner Gate to the Gate of Ephraim was about 580 feet. Since the Ephraim Gate was obviously in the north, so must be the Corner Gate. The corner gate was on the western corner of the Temple Mount, on the opposite side of the Tower of Hananel (Jeremiah 31:38-9), which was at the farthest part of Jerusalem northward. The Ephraim Gate must therefore have been that on the NE corner of the present Muslim platform of the Dome of the Rock. The Benjamin Gate was on the northeast corner of the Temple Mount, near the Tower of Hananel, probably to the west of the Golden (Sheep?) Gate. The Gate of the Guard was somewhere S. or E. of the Sheep Gate. The Old and Fish Gates (Nehemiah 12:39) were somewhere in between the Corner and Ephraim Gates. The Horse Gate was the gate at the SE corner of the Temple Mount (Jer 31:40, 2 Kings 11:16). The gates outside those of the Mount were built by Jotham (or Uzziah).
The east gates, the Fountain Gate and Water Gate, are pretty easy to figure out, the Water Gate being the gate leading to the Gihon somewhere on the southeastern Ophel or the narrow area between Ophel and the City of David, and the Fountain Gate being the SE gate of Jerusalem (Nehemiah 3:26, 12:37).
The Valley (Gai) Gate (Nehemiah 2:13) was on the southwest, bordering the Valley (Gai) of Ben-Hinnom, due to the fact if it led east it would be called the Brook (Nakhal) Gate. The Refuse (Dung) gate was roughly 1450 feet away from the Valley Gate toward the east (Neh 3:13), probably at the southernmost point of Jerusalem, the Dragon’s (Serpent’s) Spring probably being the Gihon, which had a dragon-related legend regarding its irregular flow in the 19th century, or, possibly, the En Rogel, or Bir ‘Ayyub, which is closer to the Refuse Gate. The potsherd gate was also at the entrance to the Hinnom (Jeremiah 19:2) and may be the same as the Refuse Gate. The Middle Gate was perhaps somewhere in the northern Broad Wall (see Jerusalem tab on this blog).