Depends entirely on what sort of event you want to host. Formal? Casual? Is there a pp budget or a neighborhood preference?
I see baby showers all the time at Alice's Tea Cup. And I have to admit it's one of my fave go to spots for a birthday, girls outing, etc. Food is terrific and even though Im pretty laid back, I dig the girlyness. I know the UWS branch has a private room, but not sure how big it is.
Alice's Tea Cup
102 W 73rd St, New York, NY 10023
See a lot of those in the private room at Brasserie 8 1/2. Think the room is the right size. Also the downstairs at Bistro Vendome (E. 58th) holds about 40 people I think.
The vagueness of your list count can be a problem for you and/or the restaurant. Was at a restaurant recently where they had reserved for 14 guests, per hostess's instructions, for a 20-somethings b'day party and an extra 9 people wandered in over next half hour or so who obviously had been invited, but had not RSVP'd and just showed up. Always a problem these days, but if the unexpected attendees overfill the room, it won't work. You will want to be careful about how many the room can really hold.
Brasserie 8 1/2
9 W 57th St, New York, NY 10019
405 E 58th St, New York, NY 10022