Lovely way to see Hyde Park or Regents or Battersea.
I'd also consider exploring Brick Lane. Lots of eye candy, fun shops, the market, galleries, etc.
Was in London over the holidays and throughly enjoyed an early morning walk with my camera as Brick Lane came to life. Be sure to stop for a pastry and tea or coffee at Kahaila. www..KAHAILA.com.
I enjoyed a scone with jam and clotted cream. Yum.
I'd also think about pre booking a tour of Parliament. Well worth the cost to see where the Government of the UK creates and debates their laws. Such an historical building.
Both of you will enjoy wandering around Liberty. Doubt either of you have seen a department store like it. Roam Carnaby Street.
A walk along the Little Venice canals to Camden Lock Market.
Absolutely investigate and ask her which of the countless London Walks she might like to take. See if she'd like mudlarking?
Are you adventurous? No fear of heights? Then consider the Tower Bridge experience.
Pay extra and arrange an inside the stones tour of Stonehenge.
It's been 20 years since I first meandered inside the circle and even with all the documentaries and historians explanations about it I remain in awe on how those stones got there. The weight, the size, the distance, their meaning. Still fascinates.
I like the vibrant Bayswater neighborhood. Close to Hyde Park and Nottinghill. 3 tube stops to chose from. Variety of buses. Walking distance from Paddington Station.
Lastly, be absolutely certain to take in Portobello Market. Go early, get there by 9am to beat the masses. Pay attention to the shops along the road as well. Many will catch your eye. Eat from a food stall. Pleasant way to spend a few hours on a Saturday morning.
Great city. Have fun!