It is Norfolk Naval Shipyard in Portsmouth, VA. In the pic she lies in the big aircraft carrier drydock of the period, number four, that sits at an angle from the others to the left (North) in the pic. The Jordan Bridge is in the Background. I've got a relative who works there. I have visited and have been down in the pump wells of DD4.*
Wisconsin lives down the road from me as well at Waterside in Norfolk, where her bow protrudes like a cutlass blade. Her nickname is "Whisky." She got that name after a 1956 collision with the destroyer Eaton extensively damaged her bow.
Luckily, the last of the Iowa-class battleships, USS Kentucky, languished nearby in Newport News Shipyard. Her contract was cancelled mid-build and they were trying to figure out what to do with her. The Navy had a portion of her bow removed and transported across the bay to Norfolk Naval Shipyard where it was joined with the Wisconsin.
As a result, she ended up one foot longer than the rest of the Iowa Class. Navy wags immediately labeled the hybrid the Wis-Ky, and that devolved to Whiskey, Wisky, or Whisky. It actually became her call sign.
Bob
* My relative came in for the Superbowl and we looked at the picture. He says it is DD4, and he should know!