Albany is a little over an hour away. Many people stay there induction weekend. Plenty of chain hotels on Wolf road (Colonie) or by the university (Washington ave and western ave). I don't know the costs. Also people have stayed in Binghamton. Also a few hotels by their university in Vestal. Don't remember the street name even though I just stayed at Comfort suites about half a mile from the university. that also would be a little over an hour away from Cooperstown. IMO, those are your best bets to check if the closer options are full or too expensive
Booked Binghamton, thanks again!