Music wise - plenty of opportunities to play, but the well paid ones are scarce. No way I'm giving up my day job any time soon.
Cost of living - higher than the US, I'd say, based on my own experience and some recent data I saw. But perhaps not hugely so. And it varies a lot from location to location, especially property prices, just as you'd expect.
NYC of England = London (even though NYC isn't your capital).
LA - we don't have one. I think Brits travelling to LA often feel quite weirded out by the experience as there's nowhere really like it over here. Over In England we have quite a few places that are known as "new towns" - Milton Keynes, Telford, Washington (yes, that's right). Los Angeles always seems to me like about 30 of our new towns scattered around in one of our more mountainous regions, joined up with freeways and then baked in scorching sun for fifty years or so, only with a few skyscapers, some nice coastline and Hollywood and all that it comes along with. I'm quite fond of LA in some ways myself, but I know of quite a few Brits who've visited your West Coast and really taken a dislike to the place. And Vegas, too (although, again, I quite like the place). We all seem to love San Francisco, though!
Anyway, over here - Birmingham is our second city (I'm about 15 miles from there and we're pretty much bang in the centre of England). Population about 2m, compared to London area at 7m. Birmingham was a bit of grim place in some ways during the 70s and 80s but still had a thriving music scene. The birthplace of metal! Economically, the place picked up a lot in the 90s due to some massive investment in key areas. It's still a pretty cool place these days to hang out, but I'm sad to report a few of our better music venues have gone in the last few years and that has had an obviously bad effect on the local scene from that point of view.
I'm sure other people will come along and add their bit about their own cities, the major ones being Manchester, Liverpool, Bristol, Leeds, Sheffield, Newcastle... These are all smaller than the first two and vary quite a bit in population size, but are often regarded as being the main cities in their respective areas. For example, Bradford has a lot more people than Newcastle, but is near to Leeds and so doesn't get to be the major city around there. But further North East, Newcastle (with its surrounding area - apologies to Gateshead and Sunderland folks) is the main metropolis. I should also mention Glasgow and Edinburgh up in Scotland (LOTS of English people have never visited Scotland and are really missing out, imo) and Cardiff in Wales.