Ride the Staten Island Ferry. The Staten Island Ferry is used daily by thousands of commuters. Ride with them for a great view of the Statue of Liberty, Ellis Island, New York Harbor, and the lower Manhattan skyline. You really can't beat the price: It's free.
Attend a Gospel Service. All around New York you'll find Sunday gospel services, but for some special soul-stirring, head to Harlem and the Abyssinian Baptist Church or Brooklyn and the Brooklyn Tabernacle. Services are free but when the basket is passed, don't be stingy.
Visit Free Museums. Believe it or not, there are museums in New York that don't charge admission. Two of my favorites are the National Museum of the American Indian and the Federal Hall National Memorial.
Take in a Game at the West 4th Street Basketball Courts, West 4th Street and Sixth Avenue. I don't know what's more entertaining: the moves on the court or the inventive, trash talk accompanying the games.