There is nowhere else like London. There is just so much to do there. Despite it being a very busy place, there are still so many places you can go and relax - Highgate Wood, the Northern Heights walk, Richmond Park etc etc. I once walked through Highgate Wood and saw about two other people in the whole time there (it was a weekday though). I really like how cosmopolitan it is, with people from all sorts of cultures (even if some bigoted people don't like all the different cultures). It also has possibly the best transport system in the world (greatly contrasting to the rest of the UK, imo!), and I am a huge fan of TfL.
The busyness of the city can get far too much sometimes, especially trying to travel by Tube at peak times. I've travelled across Europe, and the only place which had such a busy and overcrowded Metro system was Paris. Travelling on the Berlin U-Bahn at peak times was like travelling on London's Tube on a Sunday morning. But the busyness is a minor thing in the grand scheme of things.
I previously lived in the London suburbs, and it was such a dreary place. If you wanted to do anything of interest, you had to catch the Tube to somewhere more interesting. I now live further from London, in Kent. With the high-speed train, it only takes me about 10 minutes more to travel to Central London. I certainly prefer living here, for the quality of life, more countryside, and beaches. I still live in a fairly 'cosmopolitan' area though which is Canterbury - a uni city with lots of different people, and a good night life. But, I still love visiting London and can always find something new to do there.