Central park: Central Park is home to 843 acres of verdant views, vibrant flora and hidden histories. enjoy a stroll or ride a bike through one of America's most famous parks. There are plenty of recreational activities and there's always something special going on in the park.
Time square: Times Square signifies everything that the city represents. The excitement, the glamour, the independent free-spiritedness and artistic qualities of New York are all on display in this timeless spot. One of the best places to begin sampling true New York nightlife.
Broadway: This is the most famous theater district in the world, represents the heart and soul of American theater.
Rockefeller Center and Top of the Rock Observation Deck: This iconic plaza has it all - beautiful sculptures, an enormous skating rink, a fishbowl view of NBC Studios, plus hordes of stores and restaurants.
The National September 11 Memorial & Museum: Serves as the primary tribute to the nearly 3,000 victims of the 2001 terrorist attacks. The Memorial's twin reflecting pools and manmade waterfalls rest as eerie footprints where the World Trade Center's Twin Towers once stood, also enclosed in bronze panels the names of every victim are inscribed.
Statue of Liberty: This brightly shining beacon draws visitors year-round. The world’s most iconic copper statue was designed by Frederic-Auguste Bartholdi as a gift from France in celebration of the nation’s centennial in 1876.
The Empire State Building: Is generally thought of as an American cultural icon. It is designed in the distinctive Art Deco style and has been named as one of the Seven Wonders of the Modern World by the American Society of Civil Engineers.
Source: http://travel.usnews.com/New_York_NY/Things_To_Do/