A district I absolutely love in London is Covent Garden. The former fruit and vegetable market hall transformed in to a shopping mall with lots of small amazing shops and bars. You can spend so much time wandering around the Piazza and the side streets.
Covent Garden is also known for it's street performances. When you go there you can always find a show of an artist which can be really funny.
London's Transport Museum is also at Covent Garden Piazza. I have not visited it yet because it's a bit pricey. Tickets cost around £13.
Here's a tip for all frozen yoghurt and muffins lovers: on my last visit I discouvered a small cafe named Muffinski's. They sell a various range of muffins with odd ingredients like potato or sweet corn for example but they also have normal ones like blueberry.
The reason I went there was to get my first frozen yoghurt ever...and well what can I say: it was so good!
You can find the cafe on King Street opposite to a Burberry store.
And for those who are searching for an internet access they offer free wifi.