I have eaten at Brooks (and had Brooks sauce at home thanks to family that lives close to Oneonta). I second Chuck's recommendation on this one.
And when I visited as a kid, we stayed in Oneonta. Not a bad drive to Cooperstown from there. The youth sports "compound" wasn't there when I was a kid, so that might add some traffic to the trip between Oneonta and Cooperstown, but it should still be about 30 mins.
If you do want to stay right in Cooperstown, the Otesaga is beautiful. We were lucky enough to get really good pricing because of my son playing in a golf tournament at Leatherstocking (state-wide youth tournament). Now that HOF weekend is over, rooms may be available again. :)
Enjoy upstate NY - it's beautiful up there (and the people are generally very friendly, nothing like NYC).
-- Dan --
Note: Please see my profile for more info regarding trading (section updated 3/4/2024). I have added a large portion of my inventory to the site, and currently have trading turned on (details are in my profile).