Here's an ideal itinerary for 7 days in London:

Day 1: Arrival and Exploration

• Arrive in London and check into your hotel
• Take a stroll through Hyde Park and visit Kensington Palace
• Head to the West End for dinner and catch a show at one of the many theaters

Day 2: Historical London

• Start the day with a visit to the Tower of London and see the Crown Jewels
• Walk across Tower Bridge and take in the views of the Thames River
• Visit St. Paul's Cathedral and climb to the top for panoramic views of the city
• End the day with a visit to the British Museum

Day 3: Shopping and Culture

• Spend the morning shopping on Oxford Street and Regent Street
• Visit the National Gallery and admire the art collection
• Take a stroll through Covent Garden and watch street performers
• Enjoy a West End show or concert in the evening

Day 4: Royal London

• Visit Buckingham Palace and watch the Changing of the Guard ceremony
• Take a tour of Westminster Abbey and learn about its history
• Visit the Houses of Parliament and Big Ben
• Take a boat ride on the Thames River and see the city from a different perspective

Day 5: Foodie Day

• Start the day with a visit to Borough Market and sample local food
• Take a cooking class and learn how to make traditional British dishes
• Visit a local pub and try some craft beers
• End the day with a dinner reservation at a Michelin-starred restaurant

Day 6: Museums and Galleries

• Visit the Tate Modern and see contemporary art
• Explore the Science Museum and learn about technology and innovation
• Visit the Victoria and Albert Museum and see the fashion and design exhibits
• End the day with a visit to the Natural History Museum

Day 7: Day Trip

• Take a day trip to Windsor Castle and see the Queen's residence
• Visit the town of Bath and see the Roman Baths
• Explore Stonehenge and learn about its history

There you have it! A week-long itinerary filled with culture, history, food, and fun.