Slo,
Second the 480 Kings Road trip...also try Picasso's Cafe on the Kings Road...a real period hang out... food is good too...its one of my breakfast places as my office is just down the road.
Vienne Westwood's workshop is just over the river in Battersea, just off Hester Road...she's there most days..a surprising place.
For fashion then Oxford Street is a trip as is Carnaby Street...a bit of a theme park now...but interesting none the less.
Certainly going to the Apollo is a history trip in itself....if she really is into music then a trip to the Abbey Road studios, on Abbey Road is essential, as is a photo on the zebra crossing.
Depending on how brave you are, not your daughter, then Soho by night is an experience.....as is a trip to parts of Hoxton, City Road etc as the new 'hip, trendy and very now London....its gradually moving east.
If its culture you want...try the Tower of London, the Tate Modern, and other museums and galleries. A trip on the London Eye, a giant Ferris wheel of an evening reveals the City at its best, followed by a stroll along the south bank.
But most of all enjoy a city where you can walk and not get done for jay walking...muggings are done with manners and you will be robbed at the cash desk in the stores...
