Would be Rubicon Recycling, Rome NY. They have only a few classics, but they try to keep them for a while if they can. very slim pickins on the MoPar front. They had a '50 Dodge 4dr for about 1-1/2 year, but gone now. It had a drive train swap before arrival.
The classics here seem to be mostly 60's, 70's.
Vince's u-pull in Marcy sometimes gets oldies in. They just go in the mix with everything else, and as far as I know go to the crusher on a time based schedule. Saw a '50 Chevy earlier this month, but did not venture over to it, as I was on a mission with limited time for sightseeing.
I have been to U-Pull U-Save in East Sry., but did not pick any classics there.