New York

Here's a suggested itinerary for 7 days in New York that meets all your constraints:

Day 1: Arrival and Friends TV Show Locations

• Arrive in New York and check into your hotel
• Head to the Greenwich Village neighborhood to see the apartment building used for exterior shots of Monica's apartment
• Visit the Friends Experience exhibit in SoHo to see recreated sets and props from the show
• Grab a slice of pizza at Joe's Pizza, a favorite of the Friends cast

Day 2: Statue of Liberty and Ellis Island

• Take the ferry to the Statue of Liberty and Ellis Island
• Explore the museums on Ellis Island to learn about the history of immigration to the United States
• Take in the views of the city from the top of the Statue of Liberty

Day 3: Central Park and Museums

• Spend the morning in Central Park, taking a stroll through the gardens and visiting the Central Park Zoo
• Visit the American Museum of Natural History to see the dinosaur exhibits and learn about the natural world
• Check out the Metropolitan Museum of Art to see world-class art and artifacts

Day 4: Times Square and Broadway Show

• Spend the day in Times Square, taking in the bright lights and energy of the city
• Visit the TKTS booth to get discounted tickets to a Broadway show
• See a show in the evening, such as Hamilton or Wicked

Day 5: Brooklyn Bridge and DUMBO

• Walk across the Brooklyn Bridge for stunning views of the city skyline
• Explore the DUMBO neighborhood, known for its trendy shops and restaurants
• Visit the Brooklyn Museum to see art and artifacts from around the world

Day 6: Empire State Building and High Line

• Take in the views from the top of the Empire State Building
• Walk the High Line, a park built on an old elevated railway line
• Visit the Whitney Museum of American Art to see contemporary art and exhibitions

Day 7: 9/11 Memorial and One World Trade Center

• Visit the 9/11 Memorial and Museum to pay respects to those who lost their lives in the attacks
• Take the elevator to the top of One World Trade Center for panoramic views of the city
• Spend the evening in the West Village, enjoying the neighborhood's charming streets and restaurants

This itinerary should give you a good mix of Friends TV show locations, main sites, and cultural experiences, all while staying within a budget. Enjoy your trip to New York!