Where to stay for 1 night in Copenhagen?

Okay.

My flight is leaving early on the next sunday from Copenhagen Airport. I should be at the airport 7:30 latest.
The night before that is saturday night, and I'm probably heading out to party and all that. That would leave me maybe 3-6hrs of time for sleeping.
Where could I stay for that one night? In a budget hostel? In some 24h internet cafe, browsing stuff online? Sleep at the airport instead?

There are hotels near the trainstation. I stayed two nights in Kopenhagen at the Absalon Hotel. Which was not that expensive. But there are more hotels in that neighbourhood. From the trainstation it's around 20 minutes to the airport, but you need some extra time to get to check-in.