You might want to consider Keens, which has been in its 36th St. location since 1885. In addition to excellent food, what sets Keens apart -- especially for out-of-town guests -- is the unmatchable charm of its old NY ambiance. If your budget could manage it, there are several gorgeous private rooms, one of which, the Lily Langtry, would be perfect for a party your size. However, even if you eat in the main diningroom, you will be surrounded by walls filled with memorabilia. Plus, of course, there are the rows of old clay smoking pipes suspended from all the ceilings, as well as pipes belonging to famous people displayed in cases in the vestibule.
Best wishes to your grandmother on her 80th birthday!
Do you want to go to the Upper East Side?
If so I highly recommend Kings' Carriage House
251 E. 82nd Street
I had my 50Th birthday party there last year, and my family and parents loved it. It has that very special feeling for a little party.
I found it one day while walking down that block, and fell in love with this carriage house and peeked inside and loved the atmosphere of this place and I asked around and heard the food was very good.
It is decorated impeccably with beautiful antiques and a small private room for your little party; they have these quaint rooms upstairs. The food is lamb chops, steaks and fish, that type of stuff. They have a price fixed menu and it was well priced for the good quality.
We were 12 people and it was great fun and the service was incredibly kind and accommodating (I have a very annoying food snooty demanding New York City family) they asked the wait staff for all types of special things and the staff always had a smile and was helpful, I liked the very private feeling of the restaurant.
You have to go look at the place, your family will love it.