Fully agree re getting downtown, well worth a visit, and Danes are a very nice people. (That`s why we like them so much, about as nice as ourselves
)
You asked about lounges, in the international terminal SAS has two, one for Business class passengers, and one for gold card holders. Free beer/wine and biccies/pastries. Diners club also has a lounge there, last time I was there (couple of years ago) they had free sandwiches too.
But do sample some of the restaurants at the airport if you spare the time.
Cheers,
AS