There's also "street pizza"
1. I'm from New Haven, so I know pizza. (My favorite in NYC is still Di Fara.)
2. Besides the serious places you've already tried, there's "street pizza" -- the run-of-the-mill pizza places you find on every block. You know, "Ray's" type stuff.
3. Try Italian Village, 80th and First in Manhattan, for the "street" genre. It's been there close to 50 years for a reason.