Drydock No. 1 has a long history and has its self been modified. From the NPS website;
"Six years under construction, the Charlestown dock was inaugurated in 1833 with the docking of Constitution. Over the course of its history Dry Dock 1 has been enlarged several times. In 1833, the dock was 341′; in 1858-60 the dock was extended to 357’; the final extension occurred in 1947- 48, when the dock became 415’ in overall length, the size that it is today."
During WWII (and for years before that) all Destroyers (and Destroyer Escorts) built at the BosNY, BIW, and Beth-Quincy were sent (or remained at BosNY if built there) to BosNY for fitting out. Fitting out normally involved at least one drydocking for finishing installation of the ship's sonar system and a dome for it (Ships couldn't be launched with a fixed sonar dome and required a drydocking to install). Other needs for drydocking included a final hull cleaning and painting prior to being sent off to war.
Post-WWII, these same WWII-built Destroyers were overhauled at BosNY and may have used the same drydock.
So a good number of WWII destroyers utilized one of the drydocks at BosNY either as new construction or during yard periods for repairs and upkeep on the hard worn convoy escorts across the Atlantic.
Prior to WWI, early cruisers could fit in Drydock No. 1. During WWI and immediately afterwards, those cruisers and the numerous destroyers built just before WWI and during WWI used the same drydock.
Which specific ships used this drydock at any give time period would require a search through deck logs.
Below is an close cropped view from a larger image of the Charlestown area of BosNY taken in February 1945. A GEARING class DDR can be seen in Drydock No. 1.