Not exactly San Jose, but my favorite New York style thin-crust is from Giovanni's Pizzeria in Sunnyvale (NOT the one in San Jose) , with Vito's Famous Pizza a near second.
Pizza Chicago is my go-to for deep dish.
I haven't tried some of places on this list, though. My answer may get edited. Time to go pizza hunting.
EDIT: I recently tried A Slice of New York and enjoyed that, too.