The original Patsy's in East Harlem has beautiful private rooms and a great coal fired oven. It's at 2287 First Avenue between 117 and 118 streets.You won't be disappointed. http://www.thepatsyspizza.com/
You don't state a budget, so I can't tell if you want a pizza joint or a restaurant that also happens to serve pizza. If it's the latter Otto does large groups and I think Peasant might as well in their downstairs room.