Off Campus, Cafeteria n Co, The Punter House, Big Yellow Door Cafe, Echoes ...all in Satyaniketan.
Satya Niketan would be the right place for you. I would suggest Big yellow door in Satya for great food and really nice and cosy ambience.
You are live in moti bagh. For birthday party many places are available near to you - Satya Niketan.
There are many restaurants and cafes are available like QD and many more. Prices are affordable and variety of food is available.