I recommend you take the S-bus (350S) out to Dragør. You can bike out there, but you have to bike home again, because there is no S-train on Amager.
The S-bus runs every 10 minutes, but remember to take the bus with the Dragør sign on.
Dragør continues to be a tourist magnet today and is one of the most attractive places to live in the Copenhagen area.
You can understand why. Beautiful 18th and 19th Century houses and gardens, little traffic, no inappropriate color schemes, no ugly new housing developments or anything else that could disturb the sense of harmony. It's like stepping back in time to an age of delightfully unthreatening uniformity, interspersed with the occasional café and pedestrianized street.
Preserving this cultural heritage was no accident, a conservation board was established in Dragør as far back as the 1920s, to safeguard the town against anything that could threaten its special character. Any renovation work or new development projects have to be in sympathy with the existing style and to this day, all new developments in the old part of the town are subject to board approval.
Efforts are also being made to add Dragør to the list of UNESCO World Heritage Sites and to ensure that nothing is sacrificed on the alter of mass tourism.
This should all enable Dragør to avoid being overrun and remain an unusually tranquil town, where people greet each other on the streets and old sea dogs still spin seafaring yarns of yesteryear. The perfect destination to travel back in time to hear birdsong, explore salt marshes in this rural idyll, a mere 12km from Copenhagen city center.