Here's a suggestive itinerary for a holiday from the UK with 3 nights in New York, 2 nights in Los Angeles, and 3 nights in Las Vegas:

Day 1: Arrival in New York City

• Fly from the UK to one of the major airports in New York City.
• Transfer to your hotel and check-in.
• Spend the rest of the day exploring the city at your leisure.
• Visit iconic landmarks like Times Square, Central Park, and the Empire State Building.
• Enjoy a Broadway show in the evening.

Day 2: New York City Sightseeing

• Take a guided tour of the city to see famous attractions like the Statue of Liberty, Ellis Island, and the Brooklyn Bridge.
• Visit the 9/11 Memorial and Museum to pay tribute to the victims of the World Trade Center attacks.
• Explore neighborhoods like Greenwich Village, SoHo, and Chelsea.
• Experience the vibrant atmosphere of Chinatown and Little Italy.
• Enjoy dinner at a local restaurant and soak in the bustling energy of the city.

Day 3: Museums and Shopping in New York City

• Spend the morning visiting world-class museums like the Metropolitan Museum of Art or the Museum of Modern Art.
• Enjoy a leisurely lunch in one of the city's trendy neighborhoods.
• Go shopping along Fifth Avenue or explore the boutiques in SoHo.
• Take a stroll along the High Line, a unique elevated park built on a former railway line.
• In the evening, dine at a rooftop restaurant with panoramic views of the city.

Day 4: Fly to Los Angeles and Explore the City

• Fly from New York City to Los Angeles.
• Transfer to your hotel and check-in.
• Spend the afternoon exploring the city's famous neighborhoods, such as Hollywood, Beverly Hills, and Santa Monica.
• Visit the Walk of Fame, the Hollywood Sign, and Rodeo Drive.
• Enjoy dinner at a trendy restaurant or sample international cuisines in a multicultural neighborhood.

Day 5: Los Angeles Attractions and Beach Time

• Visit popular attractions like Universal Studios or the Getty Center.
• Enjoy some leisure time at one of Los Angeles' beautiful beaches, such as Venice Beach or Malibu.
• Engage in water activities like surfing or paddleboarding.
• Watch the sunset over the Pacific Ocean and enjoy a beachside dinner.

Day 6: Fly to Las Vegas and Explore the Strip

• Fly from Los Angeles to Las Vegas.
• Transfer to your hotel and check-in.
• Spend the day exploring the famous Las Vegas Strip, known for its iconic hotels, casinos, and entertainment venues.
• Visit themed resorts like The Venetian, Bellagio, or Caesar's Palace.
• Enjoy a dinner buffet at one of the renowned hotels.
• Experience the vibrant nightlife and entertainment options in Las Vegas.

Day 7: Day Trip to the Grand Canyon

• Take a day trip to the Grand Canyon, one of the world's natural wonders.
• Enjoy breathtaking views of the canyon from different viewpoints.
• Take a helicopter or airplane tour for a unique perspective.
• Explore the rim trails and learn about the geology and history of the area.
• Return to Las Vegas in the evening and enjoy a show or try your luck at a casino.

Day 8: Las Vegas Free Day and Shopping

• Use this day to relax and enjoy the amenities of your hotel, such as pools or spas.
• Explore the various shopping options in Las Vegas, including high-end boutiques and outlet malls.
• Visit the iconic Las Vegas sign for a memorable photo opportunity.
• Enjoy a farewell dinner at a celebrity chef's restaurant or indulge in a lavish buffet.

Day 9: Departure

• Enjoy your final breakfast in Las Vegas.
• Check out of your hotel and transfer to the airport for your return flight to the UK.

Please note that this itinerary provides a general framework for your holiday, and you can customize it based on your preferences and the specific activities and attractions you wish to include.