The two best day trips from Esbjerg are very different. Ribe, half an hour south by car or train, is the oldest town in Denmark — a perfectly preserved medieval cathedral town and one of the most attractive places in Jutland. Billund, an hour and a quarter inland, is the home of Lego and Legoland and the obvious family stop. For a half-day, take the ferry across to Fanø: dunes, a long Wadden Sea beach, and two villages of skipper-houses that look as they did two centuries ago.
