You've heard about the reading room at the New York Public Library, haven't you? Then I need not go on. Just look at it. And you're allowed to hang around in there!
Within an couple hours' drive of NYC, you can find lots of sleepy seaside towns. Not only can you get your soft ice cream and salt water taffy on, but you can still spot cool, hand-lettered signs and other relics of a past generation's amusements.