Band Baja Barat and duty free both are good for birthday celebration with family. Both are in rajouri garden. Price around 1200 rs buffet each person.
Try out Chili's in Pacific Mall it's very good with a nice ambience or you can visit barbeque nation near you for the buffet system to spend quality time with your family.
Jungle jumboree or flavours from heaven
Pirates Of The Grill is a great option. From what I know they also have a party lounge on the first floor. So, you might want to call them up and check!
Over The Top in Janakpuri is family friendly and does great food. Must try the Dahi ke Sholey!