Cafe Frick has a good, small seasonal menu of salads and well-prepared entrees and serves a classic high tea. They always have at least one vegetarian item on the menu, and it's consistently excellent. The room has lovely views of the Frick estate (you can sign up for a tour of the house if you want), and it's steps from the Frick art gallery which has a nice, little permanent collection of 17th-19th c. European art and hosts some great small travelling shows, too. The cafe is often booked to capacity at peak hours, so it's a good idea to reserve, even for lunch and tea. (Note: If you're not member they will only take your reservations up to 48-hours in advance.) Be warned, though, the people who take phone reservations are snotty and off-putting, but once you're there, most of the waitstaff is pleasant enough. A great place to take Mom.
Pros: Nice room, beautiful views, good food
Cons: Service can be snotty