I second that you want to get a hotel to stay the night.
If that is not an option .. or you think it is too expensive (Hotels in del are expensive) then another choice is the departure visitors lounge area outside the terminal.
It is functional, crowded but most people can find a place to sit and get some coffee/tea/snacks.
Again .... its functional ... nothing fancy (Cost is around Rs 100 to get in i think .... i have never used it but parents of a friend of mine who did not want to travel home late at night used it for a few hours on their return from the US)