Danny's Market on Main Street is great for bagels and sandwiches, hot or cold. The Reuben sandwich was a little different from a standard Reuben, but it was tasty, toasty and good. Also try their "breakfast burrito" -- it's not really a burrito, but more like a wrap-style sandwich filled with scrambled eggs, potatoes, and a little salsa. Yum. It hits the spot. Coffee's good too.
Schneider's bakery on the corner of Chestnut and Main is like Norman Rockwell's America (well, the whole town is pretty much like that too).
Doubleday Cafe is usually good, sometimes just OK. We love their curly fries. But burgers are small. And the cafe is small and tends to get very crowded.
The tiny Cooperstown Diner (so small you might miss it on Main Street) oozes retro charm-- but, on the morning we were there, they were terribly understaffed...only one guy cooking, and one very young woman handling everything else (taking orders, serving, refilling coffee mugs, bussing tables, AND doing cash register --whew). We had a long wait for breakfast and the food arrived cold. But, the coffee was good and the ambiance ... well, more Norman Rockwell.
Cooley's Tavern (on Pioneer Street, about a block off Main) had really really good homemade New England clam chowder on the rainy night we were there.
Foo Kin John Chinese take-out (across Pioneer Street from Cooley's) had lo mein that made my teenaged son happy when he got the hungries late at night.
And yes, do go to the Fly Creek Cider mill a few miles to the west of Cooperstown. Lots of goodies to eat there, and the cider is fresh from the apple press and out of this world.