Surrounded by lime trees, handsome, red-brick Sankt Olai Domkirke is a Gothic cathedral built in 1559. Eclectic features include an over-the-top white-and-gold altarpiece (one of Denmark’s largest at 12m high), an ominous black stone slab where the names of wrong-doers were written, and, wedged in an archway, an English cannonball fired en route to the Battle of Copenhagen (1801).