Depends what you mean by close and also what you mean by casino. There is a tribal casino, Turning Stone, near to Syracuse, NY, about 65 miles away from Cooperstown. Gaming is resticted to certain games and certain types of slot machines.
Here is a link to their web site:

http://www.turning-stone.com/

The closest full gaming casinos to Cooperstown are in Connecticut, Mohegan Sun and Foxwoods, about 230 miles away.

Atlantic City casinos are 325 miles away.