I was born and bred in London before living in Stockholm for a few years, Dusseldorf for 2 etc. I've worked and stayed for extended periods in Amsterdam, Berlin, Budapest, Hamburg, Frankfurt, Barcelona, Valencia, Rome, Florence, New York, Istanbul...(the list goes on)....
Every international city has it's own characteristics but ultimately they all share 2 common things, a unique cultural 'vibe' / identity (the style of the buildings, the food you can eat there etc) and 1 other thing:
tourism.
London is unique in the fact that it
has everything from every place you could ever imagine. London evolved as a series of smaller villages ("hamlets") that all had their own unique characteristics that slowly grew to merge together. Combine that with the British empire and the way the country was in essence founded over many centuries of immigration and pooling of resources from every corner of the world and you have one big melting pot of culture where you can pretty much see, do, buy, eat anything you want to.
They say if you're bored of London you're bored of life, in 30 years I haven't seen everything and I was born here, so how anyone could ever see everything in a week, 2 weeks, month, year I have no idea, you can't call it shit, you're just in the wrong part of London.
I've lived North, South, East and West and I live in
Chiswick as of the past 2 years, down the road from where I was born, I wouldn't want to live anywhere else now. There are parts of London I hated living in (especially East London), but each area is so drastically different from another there's always somewhere that will suit someones personality.
The same applies to every other city I've visited, Amsterdam for example is an awesome city in the centre, go to west Amsterdam though and it's a completely different place, it's a fucking shit hole. Does that make Amsterdam shit? No, it doesn't.
Contrary to what people think we're a very chatty city and we do talk to people (it's true everyone's always in a hurry though), all too often people rely on tour guides and manufactured tourism maps to direct them to the usual crap instead of telling you to go off the beaten track, the best way to see a city this size is by asking someone who's from here.