It's a shithole, OP.
Most of the infrastructure is Victorian, so the roads aren't wide enough for the traffic, the street plan is all over the place, the pavements aren't wide enough for the amount of people, the Tube trains can't carry the amount of passengers, there aren't enough railway lines, etc. London exists in an almost permanent state of gridlock for any given means of transport. The buses are also overcrowded. Cyclcing is quite literally terrifying.
Also, travelling by tube is very slow. In some stations it can take 10 minutes just to walk down to the platform, and while it feels like you're going quite fast when you're on the train, it actually crawls along at a snail's pace. In many places, if you're only going one stop, it's quicker to walk.
Everything central shuts down at midnight. It's quite the culture shock if you've come from a 24 hour city. That includes most of the tube network, which means you have to either get a taxi, or get the night bus, which is usually full of loud drunks and a sense of vague unease.
Violent crime is pretty bad in all central boroughs, as is car crime and burglary. However, the murder rate is low compared to US cities. Homophobic crime is increasing, especially in East London, but it's still quite low. It's much quieter in the suburbs.
Houses are tiny, and very expensive. You won't get a house in a remotely decent area for less than £1m. If you do manage to find one, check it out on streetview because it will probably be right next to a really rough estate. Apartments are easier to find for less than that. However, the same rule applies to check it on streetview, and unless it's a new building, it is unlikely to have either a lift or parking. In fact, parking is generally a nightmare unless you have a driveway, which most houses don't. Usually it's on street parking with a permit-only scheme that allows one car in front of your house, which can make it very difficult to have friends round. Houses usually also have no garden, or a very small one.
It's also very hard to say what is a nice area. All of the boroughs have nice parts and horrible parts. The councils have a tendency to put rough etates right next to nice streets, so even living somewhere like Kensington is no guarantee it'll actually be nice.
Like all English cities, it looks nice if you don't look at anything for too long. If you do, you start to notice that everything is actually quite scruffy; the houses are all stained by the huge amount of air pollution, the pavements are often a random (and uneven) patchwork of paving slabs, concrete and tarmac, ugly brutalist architecure is plonked right next to grand old terraces, skyscrapers seem to pop up everywhere with no apparent congruence, front gardens have all been paved over for parking, there's litter everywhere, and so forth.
Eating out can be found quite cheaply if you aren't that picky. If you are, it's very expensive, as is drinking. The gay scene is also spread out over the city, so you need to travel between venues. In Soho, it's all in one place, but then Soho tends to attract a younger crowd, and shuts down at midnight.
It's true that some parts of the East End do look like Karachi. Whether that's an issue, is entirely up to you.
As an American, you'll be quite surprised how rude people are, and how poor customer service is.