I can't imagine a trip to London without a visit to Kensington Palace. Sure, I harbor a small fantasy of running into KP resident Kate Middleton and Lupo on one of their walks, hitting if off, and deciding to grab a cup of tea together. Nevertheless, there are some fabulous exhibitions, like Victoria Revealed, all about Queen Victoria's life and how she lived it after losing her beloved Albert, laying out his clothes every day until the day she died (I just realized they were first cousins. Ew. But perfectly acceptable in their day).
This summer, a new exhibit opened called Fashion Rules, showing off dresses from the collections of Queen Elizabeth II, Princess Margaret (her hard-partying, gal-about-town sister), and Princess Diana. While the exhibit is small, I always enjoy seeing dresses in person and marveling at the tiny waists and fashion evolutions. Really, Diana's red dress on display can only be described as in the style of a Christmas ornament.
If you have time before or after your visit to the palace, The Orangery at Kensington Palace is one of the best places for afternoon tea in London. Built by Queen Anne, the 18th-century Orangery was the setting for royal parties and today still has a beautiful white interior and bright light.
I also love Kensington Gardens, which is adjacent to Hyde Park. I stayed at the lovely Royal Garden Hotel, which allowed me to wake up early and stroll the gardens, pretending like I lived in London. Save time to sit in the Italian Gardens, with gorgeous fountains and sculptures.