see here in the states New York style pizza is the original thin cardboard crust stuff you have to fold to eat it, where as the deep dish , so thick you have to eat it with a fork is Chicago style. Guess which is my favorite.
Mark, I'm pretty sure you're talking about New York Pizza - http://www.newyorkpizza.nl/ they're all over the city and I personally think they're pretty good for grabbing a slice on the go!
As for calzones, the best place I know is Da Vinci's Calzone next to Greenhouse Namaste - http://www.calzoneking.nl , best calzone I've had anywhere!
I enjoy the Da Vinci calzones as well. Damn Tasty is great (new york pizza.nl) But there is a late night place as well....hrm it's listed on http://www.thuisbezorgd.nl/ along with all the other delivery.