East Jutland : Samsø
Samsø is a quite island mid way between Zealand and the Jutland peninsular, not making much noise about itself. Nationally its main claim to fame is the first potatoes of year always hails from the island, while it has more recently garnered international attention since the heat and energy used on the island is exclusively produced by renewable sources.
While it is possible to grab a taxi flight from Roskilde Airport to the islands small airfield, the 2900 DKK Samair charges for single flight with up to 3 passengers, leaves the vast majority taking one of the two ferries connecting to the island.
Samsøtrafikken ferries departs Kalundborg on Zealand to Kolby Kås on the islands west coast up to seven times per day between 6.40 and 20.15 on weekdays. The crossing takes an hour and fifteen minutes. Tickets costs 98 DKK for a one way passenger ticket, and 281 DKK for a car. To Kalundborg there is direct train connections from Copenhagen once or twice per hour depending on the time of day.
The same company also runs ferries from Hov south of Århus to either Sælvig or Kolby Kås every two hours between 8 - 20. This crossing takes an hour and tickets cost DKK 86 for a single passenger ticket, and DKK 375 for a car. There is a bus service directly between Århus and the harbour (line 103).