a trip to the waterfront is ok. There is a small boat port, with bars either side, that is pretty busy. Take the sightseeing barge on a tour to kill some time.
you can also get a train to Sweden from the main station in Copenhagen. The trip takes about an hour. Malmo has a busy square near the station but the beer is even more expensive over there.
the cheapest beer was in the stadium but that did mean loads of drunks by the end of the gp so the atmosphere wasn't that friendly on the exit roads
hope you like sausages, a van on every corner, and have plenty of money as Denmark isn't cheap.
good gp so you should have a nice weekend