Dunno if Saratoga Springs is close enough for you, but 9 Maple is a classic (no food), and Max London's bar offers terrific cocktails, like a Manhattan with Sazarac rye and Vya vermouth. Can't speak with any authority about Albany proper, although I've enjoyed the cocktails at the bar at Angelo's 677 Prime quite a lot.
Max London's Restaurant
Saratoga Springs, NY, Saratoga Springs, NY
Angelo's 677 Prime
677 Broadway, Albany, NY 12207