It’s hard to imagine, as you stroll Heimaey’s idyllic streets of white wooden houses, that this island was literally torn apart by a spectacular volcanic eruption, just over 40 years ago. The fact that you can visit incredible Heimaey at all is something of a miracle – because the oozing lava of the Eldfell volcano threatened to seal the harbour off completely. Fortunately, its advance was halted by gallons of seawater, pumped onto it by the plucky islanders, who saved their fishing industry in the process. Iceland’s famous for its scenery, and the huge castles of volcanic rock that rise out of the sea’s waves here are some of the country’s most dramatic.

Founded by Dutch fishermen in the 17th century, Lerwick today is a busy town and administrative center. Handsome stone buildings—known as lodberries—line the harbor; they provided loading bays for goods, some of them illegal. The town’s twisting flagstone lanes and harbor once heaved with activity, and Lerwick is still an active port today. This is also where most visitors to Shetland dock, spilling out of cruise ships, allowing passengers to walk around the town.

With close to 220,000 inhabitants, Aberdeen is Scotland’s third most populous city. Locally quarried grey granite was used during the mid-18th to mid-20th centuries for many of Aberdeen’s buildings, and hence the nicknames it has earned as the Granite City, or the Grey City. Aberdeen granite was also used to build the terraces of the Houses of Parliament and Waterloo Bridge in London. Since the discovery of North Sea oil in the 1970s, Aberdeen has also been called the Oil Capital of Europe or the Energy Capital of Europe. It is no wonder that because of the oil fields in the North Sea, Aberdeen’s seaport is very important. The Heliport with its flights to the oil fields is one of the busiest commercial heliports in the world.

Edinburgh is to London as poetry is to prose, as Charlotte Brontë once wrote. One of the world’s stateliest cities and proudest capitals, it’s built—like Rome—on seven hills, making it a striking backdrop for the ancient pageant of history. In a skyline of sheer drama, Edinburgh Castle watches over the capital city, frowning down on Princes Street’s glamour and glitz. But despite its rich past, the city’s famous festivals, excellent museums and galleries, as well as the modern Scottish Parliament, are reminders that Edinburgh has its feet firmly in the 21st century.Nearly everywhere in Edinburgh (the burgh is always pronounced burra in Scotland) there are spectacular buildings, whose Doric, Ionic, and Corinthian pillars add touches of neoclassical grandeur to the largely Presbyterian backdrop. Large gardens are a strong feature of central Edinburgh, where the city council is one of the most stridently conservationist in Europe. Arthur’s Seat, a mountain of bright green and yellow furze, rears up behind the spires of the Old Town. This child-size mountain jutting 822 feet above its surroundings has steep slopes and little crags, like a miniature Highlands set down in the middle of the busy city. Appropriately, these theatrical elements match Edinburgh’s character—after all, the city has been a stage that has seen its fair share of romance, violence, tragedy, and triumph.Modern Edinburgh has become a cultural capital, staging the Edinburgh International Festival and the Fringe Festival in every possible venue each August. The stunning Museum of Scotland complements the city’s wealth of galleries and artsy hangouts. Add Edinburgh’s growing reputation for food and nightlife and you have one of the world’s most beguiling cities.Today the city is the second most important financial center in the United Kingdom, and the fifth most important in Europe. The city regularly is ranked near the top in quality-of-life surveys. Accordingly, New Town apartments on fashionable streets sell for considerable sums. In some senses the city is showy and materialistic, but Edinburgh still supports learned societies, some of which have their roots in the Scottish Enlightenment. The Royal Society of Edinburgh, for example, established in 1783 “for the advancement of learning and useful knowledge,” remains an important forum for interdisciplinary activities.Even as Edinburgh moves through the 21st century, its tall guardian castle remains the focal point of the city and its venerable history. Take time to explore the streets—peopled by the spirits of Mary, Queen of Scots; Sir Walter Scott; and Robert Louis Stevenson—and pay your respects to the world’s best-loved terrier, Greyfriars Bobby. In the evenings you can enjoy candlelit restaurants or a folk ceilidh (pronounced kay-lee, a traditional Scottish dance with music), though you should remember that you haven’t earned your porridge until you’ve climbed Arthur’s Seat. Should you wander around a corner, say, on George Street, you might see not an endless cityscape, but blue sea and a patchwork of fields. This is the county of Fife, beyond the inlet of the North Sea called the Firth of Forth—a reminder, like the mountains to the northwest that can be glimpsed from Edinburgh’s highest points, that the rest of Scotland lies within easy reach.

About 8 miles downstream—which means seaward, to the east—from central London, Greenwich is a small borough that looms large across the world. Once the seat of British naval power, it is not only home to the Old Royal Observatory, which measures time for our entire planet, but also the Greenwich Meridian, which divides the world into two—you can stand astride it with one foot in either hemisphere. Bear in mind that the journey to Greenwich is an event in itself. In a rush, you can take the driverless DLR train—but many opt for arriving by boat along the Thames. This way, you glide past famous sights on the London skyline (there’s a guaranteed spine chill on passing the Tower) and ever-changing docklands, and there’s usually a chirpy Cock-er-ney navigator enlivening the journey with his fun commentary. A visit to Greenwich feels like a trip to a rather elegant seaside town—albeit one with more than its fair share of historic sites. The grandiose Old Royal Naval Hospital, designed by Christopher Wren, was originally a home for veteran sailors. Today it’s a popular visitor attraction, with a more glamorous second life as one of the most widely used movie locations in Britain. Greenwich was originally home to one of England’s finest Tudor palaces, and the birthplace of Henry VIII, Elizabeth I, and Mary I. Inigo Jones built what is considered the first “classical” building in England in 1616—the Queen’s House, which now houses a collection of fine art. Britain was the world’s preeminent naval power for over 500 years, and the excellent National Maritime Museum> details that history in an engaging way. Its prize exhibits include the coat worn by Admiral Lord Nelson (1758–1805) in his final battle—bullet hole and all. The 19th-century tea clipper Cutty Sark was nearly destroyed by fire in 2007, but reopened in 2012 after a painstaking restoration. Now it’s more pristine than ever, complete with an impressive new visitor center. Greenwich Park, London’s oldest royal park, is still home to fallow red deer, just as it has been since they were first introduced here for hunting by Henry VIII. The Ranger’s House now houses a private art collection, next door to a beautifully manicured rose garden. Above it all is the Royal Observatory, where you can be in two hemispheres at once by standing along the Greenwich Meridian Line, before seeing a high-tech planetarium show. Toward north Greenwich, the hopelessly ambitious Millennium Dome has been successfully reborn as the O2 and now hosts major concerts and stand-up comedy gigs. More adventurous visitors can also go Up the O2 on a climbing expedition across the massive domed surface. Meanwhile, those who prefer excursions of a gentler kind may prefer to journey a couple of miles south of the borough, farther out into London’s southern suburbs, to the shamefully underappreciated Eltham Palace. Once a favorite of Henry VIII, parts of the mansion were transformed into an art deco masterpiece during the 1930s.