The five boros are full of Italian social clubs. If you go for a stroll on 18th ave. in Bensonhurst you'll find plenty. Figli di Ragusa, Santa Rosalia, Lentini Club, Aidone Club, etc...
Red Hook, Carroll Gardnes, Cobble Hill and Billyburg too. My favorite is the Citizens of Pozzallo club on Henry street. Not far from that there's the Molese Club and further down there is a tiny bar\possible club filled (as July 2010) with youngish Italians (mostly connected to the larger Molese Club I suppose).
The only time when this places are visitable by non-members is during the centennial feast of la Madonna SS Addolorata (Our Lady of Sorrows) since that is the patron saint of Mola di Bari. The statue gets carried around and it stops in front of each club or italian-owned business.
I dunno about Manhattan, Queens or the Bronx, but I don't have to guess.
Yonkers has three big ones, one is the one I call the Salerno Club, since that most members I met where from the Salerno province and I can't recall its actual name. No clue about the other two.
And don't even get me started with Staten Island...or North Jersey.
North Hempsted, Long Island has a nice club\ballroom dedicated to la Madonna Assunta. Bathpage has a couple.
Now, knowing which one of these is mobbed up (fully or partially) then it's hard to say.
But to answer your question, yes, there are a lot.
