Here's a suggestive itinerary for a 3-night trip to Iceland, followed by 3 nights in Niagara Falls, and finally 3 nights in New York City:

Iceland Itinerary:

Day 1:

• Fly from the UK to Reykjavik, Iceland.
• Arrive in Reykjavik in the morning or early afternoon.
• Check into your accommodation and freshen up.
• Spend the day exploring Reykjavik's vibrant city center, visiting landmarks like Hallgrímskirkja, Harpa Concert Hall, and the Old Harbour.
• In the evening, enjoy dinner at a local restaurant and try traditional Icelandic cuisine.

Day 2:

• Take a full-day guided tour along the Golden Circle, which includes stops at Thingvellir National Park, Geysir geothermal area, and Gullfoss waterfall.
• Marvel at the stunning natural landscapes and geological wonders of Iceland.
• Visit the famous Geysir, where you can witness the Strokkur geyser erupting.
• Enjoy the beauty of Gullfoss, one of Iceland's most breathtaking waterfalls.
• Return to Reykjavik in the evening and spend the night exploring the city's nightlife or relaxing at a local hot spring.

Day 3:

• Embark on a thrilling adventure by taking a guided tour to explore Iceland's southern coast.
• Visit the stunning Seljalandsfoss and Skógafoss waterfalls.
• Explore the black sand beach of Reynisfjara and admire the basalt column formations.
• Optional: Take a glacier hike or visit the Jökulsárlón Glacier Lagoon (requires a longer tour or additional day).

Day 4:

• Check out from your accommodation in Reykjavik.
• Transfer to the airport for your flight to Niagara Falls, Canada.

Niagara Falls Itinerary:

Day 4:

• Arrive in Niagara Falls and check into your hotel.
• Explore the town and take a leisurely stroll along the Niagara Parkway.
• Experience the incredible views of the falls from various vantage points.
• Enjoy dinner with a view at a restaurant overlooking the falls.

Day 5:

• Take a boat tour, such as the Maid of the Mist or Hornblower, to get up close to the falls and feel the mist on your face.
• Visit the Journey Behind the Falls attraction for a unique perspective of the cascading water.
• Explore the Clifton Hill area, filled with entertainment options like arcades, museums, and shops.
• In the evening, enjoy the illuminated falls during the nightly light show.

Day 6:

• Take a day trip to Niagara-on-the-Lake, a picturesque town known for its wineries and charming atmosphere.
• Visit local vineyards for wine tastings and enjoy a leisurely lunch.
• Explore the town's historic sites, boutiques, and gardens.
• Return to Niagara Falls and spend the evening at your leisure.

Day 7:

• Check out from your Niagara Falls hotel.
• Cross the border to the United States and transfer to New York City.

New York City Itinerary:

Day 7:

• Arrive in New York City and check into your hotel.
• Start your NYC experience by exploring Times Square, a bustling hub of entertainment and bright lights.
• Visit iconic landmarks like the Empire State Building and Rockefeller Center.
• Enjoy dinner at a local restaurant and soak in the vibrant atmosphere of the city.

Day 8:

• Take a full-day sightseeing tour of New York City, covering popular attractions such as Central Park, Statue of Liberty, Ellis Island, and the 9/11 Memorial.
• Explore neighborhoods like Greenwich Village, SoHo, or Chelsea.
• Enjoy a Broadway show in the evening or attend a live performance at Lincoln Center.

Day 9:

• Spend the day exploring world-class museums such as the Metropolitan Museum of Art or the Museum of Modern Art.
• Visit the High Line, an elevated park built on a historic freight rail line.
• Go shopping on Fifth Avenue or explore the trendy boutiques in the SoHo district.
• In the evening, dine at a trendy restaurant or enjoy a rooftop bar with panoramic views of the city.

Day 10:

• Check out from your hotel.
• Depending on your flight time, you may have a few hours for some last-minute shopping or exploring.
• Transfer to the airport for your return flight to the UK.

Please note that this itinerary provides a general framework for your trip, and you can adjust it based on your preferences and interests. Also, be sure to check the latest travel restrictions, guidelines, and opening hours of attractions in each destination before your trip.