I am not that familiar with that area, I suspect there are some unheralded gems along the way. One that is slightly out of the way depending on your travel route would be Otesaga in Cooperstown. There has been discussion here on its merits of being included in the top 100. I don't think that is the case but it's an old quirky course with lots of scenic views. It's pretty much in town. Also home of Baseball Hall of Fame?
If you want to go via Albany instead of up through Bingamton there are some nice ones including one featured last year here Mohawk Golf Club.
There are a couple well regarded courses in the Binghampton area; Hiawatha Landing and Conklin Players club. I haven't played either but Hiawatha gets nice reviews but it's not a golden ager.
There very well may be something in the Elmira, Horseheads area, that is the home of PGA player Joey Sinclair and someone else who's name escapes me.
I'll try and think of more. While out of your way I could likely host a round in the Albany area. I am at Normanside Cuntry Club, quirky but certainly not golden age. I could arrange pretty much anything in the area. Golden age would be Mohawk, Schuyler Meadows, Wolferts Roost?
Dan