Here's an ideal itinerary for 2 days in New York:

Day 1:

• Start your day with a visit to the iconic Statue of Liberty. Take a ferry ride to Liberty Island and enjoy the stunning views of the city skyline from the top of the statue.
• After that, head to the 9/11 Memorial and Museum to pay your respects to the victims of the tragic event. The museum is a somber but important experience that will leave you with a deeper understanding of the impact of the attacks.
• For lunch, head to Chelsea Market, a food hall with a wide variety of delicious options. You can find everything from sushi to tacos to lobster rolls.
• In the afternoon, take a stroll through Central Park. This massive park is a peaceful oasis in the middle of the bustling city. You can rent a bike or take a horse-drawn carriage ride to explore the park's many attractions.
• For dinner, head to Times Square and try one of the many restaurants in the area. After dinner, catch a Broadway show or take a walk through the brightly lit streets.

Day 2:

• Start your day with a visit to the Empire State Building. This iconic skyscraper offers stunning views of the city from its observation deck on the 86th floor.
• After that, head to the Metropolitan Museum of Art. This massive museum has an incredible collection of art from around the world, including works by famous artists like Van Gogh and Monet.
• For lunch, head to Katz's Delicatessen, a New York institution that's been serving up delicious sandwiches since 1888.
• In the afternoon, take a walk across the Brooklyn Bridge. This iconic bridge offers stunning views of the city skyline and is a great way to get some exercise while taking in the sights.
• For dinner, head to Little Italy and try some authentic Italian cuisine. After dinner, take a walk through the neighborhood and enjoy the lively atmosphere.

There you have it! With this itinerary, you'll be able to see some of the most iconic sights in New York while also experiencing the city's unique culture and cuisine.