It really depends on how long you are staying in Cooperstown. You do need reservations well in advance for the summer. I have a summer home near there so I haven't used a hotel in a while except in winter but there is a website
www.cooperstownstay.com that covers hotels, lodges, bed and breakfasts and even rental of private homes. Problem is that with tourism and Dreams Park tournaments, they fill up fast and its hard to find a room for less than a week.
Lots to do there though, in addition to the HOF, there is always a game at Doubleday Field and great fishing and boating on Otsego Lake.