Trip To India.. Help! (New Delhi)

Hello everyone!! I'm planing a trip to India on New Years basically, we're a group of Protected content looking for something cheap, clean and fun!! People are suggesting New Delhi for new years eve and Goa for the rest of the trip but we're still not sure.. Anyone got any suggestions??! We're not looking to stay in 5 star hotels, basically more of a backpacking chilled trip..
Thank a lot =)