No one would have predicted that this small room, which began as a coffeehouse and almost immediately segued into a full-fledged restaurant, would become such a popular spot. Perhaps it's the intimacy of the place, with its mere 38 seats. Even though--or perhaps because--the tables are so close together, the room has an appealing energy. The well-prepared food, on a menu that's the right length for a bite-size restaurant, includes eight appetizers, a half-dozen pasta dishes and five main plates, notable among which are tournedos di vitello, medallions of veal filet in a fresh mushroom sauce. Cafe Nini is named for Alicia (Nini) Barbieri, the third generation of the Da Edoardo restaurant family.