Haven't been in ages so can't vouch for it recently, but my dad's favorite restaurant for his birthday dinner was Fiorini on East 56th. Very old school in decor, menu, and service. Dad loved telling the waiters exactly how he wanted his Fegato a la Veneziana, and he always got it the way he wanted it--even if it wasn't on the menu.
Here's a link to the menu: http://menupages.com/restaurants/fior...
209 East 56th Street, New York, NY 10022