Every American that I know that has come to London has loved it here. I'm proud to say that I'm from LDN; the most culturally diverse city in the world and we're trendsetters.
Anything you want you can find it here, and whatever scene you like, we got it. If Hip Hop, Indie/Hipster, Skateboard, Artsy shyt is yor thing then check out central-east London (Shoreditch/Brick Lane/Old Street/Dalston), it's often described as London's answer to Lower-Eastside New York; very non-conformist and chilled. The street parties and rooftop BBQs are too dope in the summer! Plus the girls that go to events in east-London are a blend of sexy and artsy dimes.
Central London is cool for touristy stuff, food and shopping. The clubs there are typical commercial/mainstream nights (places like Tiger Tiger, Rainforest, etc), but that's not so much my kind of flavour (I'm definitely a Hip Hop/ Neo-Soul and House in Shoreditch kinda person).
North London has Camden which is a pretty cool place to find unusual alternative stuff to buy in the Market, but I don't really go to any other parts of North much, as there doesn't seem to be much else (no offense North heads lol).
West is cool; you got the huge shopping centre Westfields (think it might be the biggest in Europe), Portobello Toad where you can buy some cool shyt and eat food from around the World, Kensignton and Chelsea are the rich people areas (£1.5m homes, Ferrari car shops kinda thing), Nottingham Hill is the infamous Carnival spot for us West Indians to represent every summer in August (pure Bachannal! Although it's not like it used it be ah tellin' yuh!)
Then there is my side of LDN, south London. It's a huge area, so there is tons to do..you'd have to see for yourself haha.
As far as chicks -- If you got an accent, it probably won't impress mug seeing as we got people from all over the world here, all the time, so I hunk many girls (and people in general) are immune to accents now. But you should be able to bag you any type of girl...the only girls you MIGHT find hard to bag are Middle-Eastern chicks.
But yeah, London is a cool city although expensive. It's at it's best in the summertime though.