Not much what you can do. The city center is just a convenient train ride away, but you need to give yourself at least 1 hour each way...We have a 5 hour layover in Copenhagen on our return trip. Since we do not have access to the SAS lounge, we'd love to hear of your ideas of how we could spend the time. We have 3 kids who will be with us.
Ok. You'll have to be quick, and there will be a lot of walking but if you are up to it here's what you do:
1) Buy Metro tickets in the Main Terminal near the exit. The metro stop is about a 100 yards away at the end of the terminal. Be sure to buy round trip tickets (return within 72 hours). See if there is a family rate. Hold on to the tickets and make sure you stamp them in the yellow machine prior to boarding (both ways).
2) Get off at the Kongons Nytorv stop in front of the Magasin (du Nord) department store near the Strøget district.
3) Stroll through the world famous pedestrian zone shopping district down Strøget toward the Stork Fountain.
4) A little past the fountain, stop in the Royal Copenhagen and Illums Bolighus (purveyor to the Danish Royalty). Buy anything at one of these two great stores for your Danish souvenir.
5) From the fountain, head south past the statue of the Danish hero Absalon and in front of the Christianborg palace. Admire the grandeur, then cross the water to Havnegade - winding your way over to the old port section - Nyhavn.
6) Take a postcard picture of the colorful row of buildings and ships. Cross the canal and keep going down Toldbodgade to the Amalienborg Palace. Note if the flag is up, showing whether the royalty is home or not.
7) Cut over to the waterfront and keep going to the left along the water - slightly past the Kastellet (fort) on the left - to the "Little Mermaid". Be amazed at how unamazing she really is - but take lots of pictures.
8) Run back the way you came - back along the waterfront, back down Toldbodgade and almost to Nyhavn. There, you'll find a small restaurant - the Told & Snaps. Walk down the steps and order lunch (they close after lunch so you timing has to be right). Order everyone a delicious open faced sandwich.
9) Bid the owners farewell, go out to Nyhavn and go up the row of colorful buildings to the Kongens Nytorv (King's New Square). Cut back over to the metro stop in front of the Magasin. Hop on the metro (be sure to stamp the ticket). Head back to the airport.
You've just experienced Copenhagen in 3-1/2 hours! Of course, this will only make you want to come back. Enjoy!