Gotta disagree with Dan a little bit: there is ALWAYS time for golf during the school year! Teugega is my favorite course that is within an hour of Syracuse. It is a very pure Ross layout, and it is a club that has a strong appreciation for its history. On the public side, Alex (a fellow Colgater) is correct: you should make the drive to Seven Oaks sometime this fall. It's a gorgeous drive from 'Cuse to Hamilton on a clear October day, and the golf course won't disappoint. If you want another day trip, Thendara (9 holes Ross, 9 holes not Ross) is a probably a 2-hour ramble, and it will be well worth, if only for the 7th and 9th greens, which are both wifty and brilliant. And of course, there is Leatherstocking--a quick use of the search function here should reveal my florid descriptions of the place (and maybe Ron can provide some photos). Turning Stone is a short hop down the thruway as well, but many (myself included) have been known to vilipend the courses there, both for their high prices and for their low quality of golf architecture.
Turning west, Rochester is a golf-rich town, and there might be a GCAer or two there who would join you for a game.