New Haven (City) has so many good restaurants! For a group of that size, I'd recommend Kitchen Zinc. They have innovative and awesome food; I'm 99% sure they have a private room. We took my parents there and they loved it. L'Orcio is Italian and has a private room that accommodates up to 45 people (according to their website) but I've never actually been there. Caseus is a personal favorite but you'd have a hard time getting that many people in there- I don't think they have a private room available.

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L'Orcio
806 State St, New Haven, CT 06511

Caseus
93 Whitney Ave, New Haven, CT 06510