Bornholm, part of Denmark and located to the east of it (and probably closer to Sweden), strikes the imagination of a lot of people. Already some 200 years ago, several painters came over to the island either to find their inspiration or to depict the beautiful rural scenery of the island, resulting in a permanent stay for a lot of them. The Bornholm School is still renowned for its still live. The most famous painters were the swedish born Karl Isaksson, who was the first of a number of artists inspired by impressionism. He was followed by a number of great painters, the most famous being Edward Weye, Olaf Rude, Niels Leergaard and the only one born at Bornholm, the incredible Oluf Høst (1884-1966). The latter lived for many years in Gudhjem, where you can visit his museum. Another great place is the Bornholms Art Museum (in danish Bornholms Kunstmuseum) which is situated some 7 km north of Gudhjem. There is a sublime costal path from Gudhjem to the Helligdomskliperne (Sanctuary Rocks) above which you find the art museum, commanding a magnificent view over the Baltic Sea towards Christians, (Christian's Island).
These days, a lot of visitors come over to Bornholm to enjoy the beaches, where the best are on the western coast between Ranne and Hasle, and on the southern coast, which has the loveliest dunes of the finest white sands, which is at it's best on the island's southern tip, Dueodde. Another great way is to bike around the island (some 100 kilometers) and to catch some fresh breath again in one of the many fields or forests or to wander around in one of the many picturesque villages. There used to be railroads on Bornholm, and where the tracks used to be are an incredible web of roads for bicycles. A great way to travel through natural scenery.
There are several interesting museums on the islands, such as Bornholms Museum with a collection on the cultural history of the islands and the ceramics museum. For botanical lovers, a visit to Erichsens Gayrd is a must. This is both a building and a garden dating from the beginning of the 19th century. If you want to have a lasting historical experience, go to Gudhjem where you can pay a visit to the Bornholms Middelaldercenter, 15 acres of 'authentic Medieval life'. Also the island is famous for it's mouth blown glass, which you can watch taking shape at Baltic Sea Glass in Saltuna, south of Gudhjem, and at various places in Svaneke, the incredibly beautiful town further south.
If you consider camping, there are a number of beautiful campsites around the island. For instance there is one at Sandvig, which is stretching up the hilside overlooking the sea, only a few km from the magnificent Hammershus Castle, which used to be the greatest fortress in Northern Europe, and which today stands high above the sea, with great natural scenery all around.
There are plenty of ferry connections to the mainland of both Sweden, Germany and Denmark. If you come from Copenhagen, there are busses and trains through southern Sweden, which connects with a hydrofoil boat to Ranne, the main town of Bornholm.