If it's a nice day take her to the park. If you're already forking out enough money on the flights and hotel, i suggest you steer clear of Harrods if in a company of a lady

Everytime i go to London i just always take a walk around Leicester and Trafalgar square, it's cooool

London Dungeons are meant to be a must as well, but havent been in over 10 years so cant really remember much.

The Thames Clipper is also just a really nice way of getting about, you get to see all the sites and it's cool especially at Sunset