From what I experienced in my week in London, I loved it. The buildings, the people, the history, it's all an incredible melding pot of culture and liveliness. I would definitely recommend going to Westminster Abbey; as a history buff, it was my favorite experience during my visit. Also, check out the British Museum, the Tower of London, the National Gallery, the Imperial War Museum, the London Eye, some classic British Pub life, and of course, places like Piccadilly Square and Big Ben.
Insider Tip:If you are converting USD to the British Pound, be strategic of how and when you choose to convert/spend your money because the British Pound is worth more than the USD so it can get pricey quick.