Itinerary for London

[FoggyFriday]

Me, DH and DD14 are flying into Heathrow early AM (landing around 8am) staying in Paddington but plan is to head straight in to see things/do things and not check in until afternoon. We're spending day 2 at Reading festival (getting train from and back Paddington) and next day we have a mostly full day free (flight around 8pm)
Can you tell us what you would suggest to do with our limited time to see and do the most/best things?

What do you like doing? Shows? Museums? Tours?

If I were you I'd do a riverboat tour, one museum and a show in the evening.

British museum is near the theatre district which cuts down on spending ages moving across London. Also covent garden is there so you can watch the street performers and have a nice coffee.