Walking the Brooklyn Bridge: Manhattan has five major bridges connecting the island to other shores, and easily the most historic and most fascinating is the Brooklyn Bridge. For a close-up look at what was a marvel of civic engineering when it was built in 1883, and a true New York experience, take the walk across the bridge from Manhattan to Brooklyn.
Taking the subway to Yankee Stadium for a Yankee game: It doesn't sound very intriguing, does it? Good or bad, there's nothing like being crammed into a subway car packed with rabid Yankee fans. And it's an experience you'll not soon forget.
Jogging around the Central Park Reservoir: Okay, you don't even have to jog it. You can walk the jogging path around the Jacqueline Kennedy Onassis Reservoir and take in the beauty of Central Park, the views of Central Park West, Fifth Avenue, and especially the skyline of midtown Manhattan.
Spending Sunday Morning in New York: This might not sound so unforgettable, but to experience the city minus the noise and activity is something special. I've noticed quite a few tourists, usually jet-lagged Europeans, wandering the parks and streets early Sunday mornings.
Walking 125th Street: Take a walk across this famous Harlem boulevard and your senses will be assaulted from the music, the variety of stores, the restaurants, the impromptu stalls selling everything from homemade CDs to fresh bean pies, the street prophets and musicians; the energy on this street is relentless.