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.
Off Campus, Cafeteria n Co, The Punter House, Big Yellow Door Cafe, Echoes ...all in Satyaniketan.
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.