Thousand-year-old Aalborg (pop. 157,000), set in the northern part of Jutland (a seven-hour drive from Copenhagen), has excellent shopping and several attractions: the North Jutland Museum of Art, the nearby Limfjord, the Monastery of the Holy Ghost, Aalborghus Castle, the house of Jens Bang (a great example of Nordic Renaissance style) and Budolfi Cathedral. Don't miss Lindholm Hoje, Denmark's largest Viking burial ground. Some of the 682 graves, which date from the ninth century, are marked by stones arranged in the shape of ships. The history of this burial site is recorded in an archaeology museum.
Aalborg is a nice, fairly relaxed place to spend a couple of days enjoying the nightlife (there are more than 200 pubs, although several maintain a reputation of late-night rowdiness), with sand dunes and beaches only an hour's drive away. Nearby, too, is Rebild National Park, 20 mi/30 km south of Aalborg, which hosts the largest Fourth of July celebration in the world outside of the U.S.
Aalborg is 140 mi/220 km northwest of Copenhagen.