If you ant to shop check out Vivien of Holloway or Collectif for new repro clothing. And of course check out the London What Katie Did store.
It really depends what your looking to do!!
There is my friends amazing rockibilly hair salon called Rockalily Cuts Shoreditch
Camden for all things quirky and vintage, filled with crazy shops and pretty much an aladins cave if you head to chalk farm markets too
The stores as Aoife said, VoH, Collectif (quite a few around London) and What Katie Did
Volupte Lounger for a create cocktail or show
Dont bother with Oxford Street unless you just want big chain high street stores but there is Selfridges there
Obviously there is loads of typical tourist stuff too
Really depends what you have in mind?!