You can go for few cafes in Hudson lane with good food ambiance and music in budget.
( Cafeteria and Co., Jack 'n' Chill, Echoes , The Hudson Cafe, Big Yellow Door)
You can throw a birthday party in any of the lounges or bars and cafes in sector 29 Gurgaon. You can even use coupons and offers available on different apps to avail good discounts. My friend recently celebrated her birthday in Ministry of Beer in sector 29 Gurgaon and her total bill was around Rs.35-40k. There were 30 people and alcohol and non-veg was also served. So you can think of celebrating your birthday in such places.