Helsingør — known to English speakers as Elsinore — sits at Denmark's narrowest point, where the Sound separates it from Helsingborg in Sweden by just four kilometres of water. It's been a strategically vital crossing since the medieval period, and Kronborg Castle, which guards the strait, is one of the most impressive Renaissance fortresses in northern Europe. Shakespeare set Hamlet here, though he probably never visited — the play cemented the castle's fame far beyond Scandinavia.
Kronborg (a UNESCO World Heritage Site) is the obvious draw, but the town itself rewards a few hours. The old quarter around Stengade has some fine 16th-century merchant houses, and the M/S Maritime Museum of Denmark — built underground inside the old dry dock next to the castle — is genuinely excellent. The frequent ferry crossing to Helsingborg makes Helsingør an easy combined trip from Copenhagen, or a convenient gateway into Sweden.