To me EWR is easier to get clear of, international arrivals-wise, and on your way into town (though JFK is better for plane-spotting).
Ride the Staten Island Ferry, walk through Greenwich Village, see a Broadway show, ride the Circle Line boat around Manhattan Island, visit MOMA, see what's going on at Lincoln Center, go clubbing in SoHo/Tribeca, stand in Times Square at midnight, go running in Central Park in the early morning, shop Fifth Avenue from 47th to 59th Street, check out Chinatown.
Hotels: my secret weapon is the Holiday Inn Midtown on West 57th. Get adjoining rooms.