What are things to do in NYC?

I am planning a trip to NY sometime in August or early September, but I don't know what to do for entertainment. I thought about seeing a Broadway show and touring sites, but I want do some specific things. Does anyone have any ideas as to what would be great things to do for a short trip (3-4 days)?What are things to do in NYC?
Go to the top of the Empire State Building, it is a very cool view of the whole city,

Take a boat tour around the city (make sure it goes by the statue of liberty)

Go to the Museum of Natural History, it is awesome and has very good exhibits, especially dinosaur ones

Go see all the fancy shops on 5th avenue

Make sure you go to Times Square (it looks awesome at night)

Supposedly "The Book of Mormon" is a cool play to see

Try and get tickets to a Mets or Yankees game

Visit Central ParkWhat are things to do in NYC?
I would definitely recommend seeing a Broadway play. I saw The Phantom of the Opera when I went a couple of years ago. It was amazing. As for other ideas, I would suggest seeing the Statue of Liberty and the Empire State Building. Since you have a short amount of time, I guess you probably wouldn't be interested in relaxing. But if you are, go visit Central Park. Also visit Time Square, which has numerous things to do. I hope this was helpful.
Yankee game. Coney Island. Walk across the Brooklyn Bridge. Ride the SI Ferry (NOT recommended during rush hour). Check out Grand Central (NOT recommended during rush hour). Times Square. Arthur Ave (the Bronx's Little Italy, much better than the Manhattan counterpart).What are things to do in NYC?
Radio City Music Hall

FAO Schwarz

Chinatown

Little Italy

South Street Seaport

Rockefeller Center

Empire State Building

Statue of Liberty
Eat

Drink

Site See

Drink

Go to the Today Show

Drink

See a Broadway Show

DrinkWhat are things to do in NYC?
Shop

Eat

Go to Times Square

Go to Broadway

Go to the parrk.

there are many things to do in NYC!!
Get me an "I %26lt;3 NY" t-shirt.