Seeking Naval Training Records

My father served in the Navy during World War II, and only recently I began to research his service aboard the USS Zircon (PY-16), on which he served for about two and a-half years, and (to a lesser degree) aboard the YMS-75.

In my research, I have been in contact with other Zircon sailors' family members who have copies of photographs of their fathers' graduation classes from training at various naval facilities. Are there records available from, say, Camp Peary, that list every name of every sailor who went through training at that facility?

I have a copy of my father's personnel file, which includes a few documents indicates training he received --  (1) "Completed Navy Training Course for SEAMAN FIRST CLASS this date with a final mark of 2.8" (2) "Completed 2 day course of instruction at Fire Fighters' School, Brooklyn, N.Y." (3) "Completed two weeks instruction  in Material of of type SF Radar Equipment at the Radar Training School for Fleet Personnel at Navy Yard, New York, N.Y."

I don't know if he received training anywhere else as these are the only documents referring to any training whatsoever, but I presume that the first one was his basic training. Where would his basic training have taken place? At the top of the form (below his date reported to the Zircon) is "From LD & DC, 3RD, Tompkinsville, NY" Was there a training facility in Tompkinsville?