There are lots of ways to do pizza. I think the two feuding styles (that matter) are New York style pizza and Chicago style pizza. Then of course you have, like, Italian pizza I guess? But that's something entirely unto itself.
Like hot dawgs, pizza joints are ubiquitous in this city. I used to be jealous of my non-vegan friends being able to grab something quick, cheap, and easy to find at all hours of the night. Maybe I still am, or maybe I should stop being out at all hours of the night. Anyway, the point is - vegan pizza places have arrived! (Or at least totally decent vegan options.)
The only one I really go to is Viva Herbal Pizza on 2nd ave between 11th and 12th st.
Tutta Verde, you can ask for sauce on top, and do. It's much better that way. G also used to go here a lot and took to bringing his own nooch, ha!
So, yeah. I'm not big on really cheezy pizza - it's more about the crust, sauce, and toppings for me. This place seems to specialize in unique toppings. If you want a more classic slice, there is Vinnie's in Brooklyn off the Bedford stop, Slice in Greenwich Village, and Pie by the Pound (also gluten free options) on 4th and 12th St.
Another nice thing about Viva is that you can get yr slice and eat it down the block outside the beautiful, historic St. Marks in the Bowery church (where Allen Ginsberg and Patti Smith and Ted Berrigan and Eileen Myles, etc. etc. have performed and New York historical figures are buried - and where my store's union meetings were held, ha!)
If you haven't picked up a dessert from Viva (or maybe even if you have), head right across the street to Stogo for vegan ice cream, hot chocolate, or local vegan baked goods.