Um, are you really from nyc? I think there's very few places in London that are seedy or dodgy by east coast standards (maybe that's me). I'd worry more about the questions that Vicky posed, these will help much more for narrowing things down (like she said, London is huge!)
I think price is the biggest limiting factor. Living in a really "good" neighbourhood can cost a fortune (as in new york of course).
It might be easier to think of neighbourhoods that are a bit "seedy" (rather than areas that are good, as most of London is fine really). But, this is a personal opinion only. I personally wouldn't live around Seven Sisters in north london, or Peckham in south london -- but I also know people who live there happily. I loved living in Brixton and Whitechapel but some of my friends weren't into it. Now I live in New Cross, which seems universally loathed, but it's fine. It's all personal preference I think.
Are you more worried about crime or ambience? Like, if an area was safe and inexpensive, but kind of rundown and not great looking, would that be okay?
Anyway London is great! Wherever you live, you'll have fun