Billy Elliot, and they are going to go to Jamie Oliver's restaurant Fifteen.
I suggested either the Victoria and Albert Museum above, which looks so cool (or the British Museum or Museum of London), and possibly either the National Gallery or the Portrait Gallery-(but maybe only briefly to get a taste).
I think hopping on the train at Waterloo Station and going to Hampton Court Palace is definitely worth the time. And a trip down the Thames to Greenwich on one of the tour boats is a great way to spend an afternoon if they have the time.
And because she and her friend are way thinner and cooler than I am, I suggested a shopping trip to Stella McCartney's store on Bruton St. in Mayfair which is just north of Berkeley Square and then continue shopping up New Bond St. and via Grosvener Square to Oxford Street. If they hit a Monsoon store, a French Connection and a Top Shop, with a stop at Selfridges and Debenham's on Oxford street, that would be fun. She already has Harrod's on her list, so she may also want to stop in at Harvey Nichols in Knightsbridge. She is a big shopper (see the cool/thin comment), so this number of stores may actually be possible for her especially if she skips some of the museums.
Anyhow, if you have any other suggestions please post below and I will pass them on. I might also suggest that hitting a pub in the Shepherd Market would be great, as would tea or a drink at The Ritz (photo above). A stroll down Piccadilly after said tea or drink at the Ritz, with a poke into the Burlington Arcade, Fortnum & Mason's and then possibly Hatchard's, -see below-(the oldest bookshop in London) would round things out nicely.
OK, if she sees even a fraction of those things, she won't have time to sleep, but it's always better to have a long list and see which ones fit into your plans. You never know where you might find yourself.
Well, you can tell what I will be dreaming about tonight. Yes, actually fitting into a Stella McCartney creation. Oh, well...a girl can dream can't she? The rest of the trip is a real possibility!