Day 1 Reykjavík, Iceland

Sprawling Reykjavík, the nation's nerve center and government seat, is home to half the island's population. On a bay overlooked by proud Mt. Esja (pronounced eh-shyuh), with its ever-changing hues, Reykjavík presents a colorful sight, its concrete houses painted in light colors and topped by vibrant red, blue, and green roofs. In contrast to the almost treeless countryside, Reykjavík has many tall, native birches, rowans, and willows, as well as imported aspen, pines, and spruces.Reykjavík's name comes from the Icelandic words for smoke, reykur, and bay, vík. In AD 874, Norseman Ingólfur Arnarson saw Iceland rising out of the misty sea and came ashore at a bay eerily shrouded with plumes of steam from nearby hot springs. Today most of the houses in Reykjavík are heated by near-boiling water from the hot springs. Natural heating avoids air pollution; there's no smoke around. You may notice, however, that the hot water brings a slight sulfur smell to the bathroom.Prices are easily on a par with other major European cities. A practical option is to purchase a Reykjavík City Card at the Tourist Information Center or at the Reykjavík Youth Hostel. This card permits unlimited bus usage and admission to any of the city's seven pools, the Family Park and Zoo, and city museums. The cards are valid for one (ISK 3,300), two (ISK 4,400), or three days (ISK 4,900), and they pay for themselves after three or four uses a day. Even lacking the City Card, paying admission (ISK 500, or ISK 250 for seniors and people with disabilities) to one of the city art museums (Hafnarhús, Kjarvalsstaðir, or Ásmundarsafn) gets you free same-day admission to the other two.

Day 2 Heimaey Island, Iceland

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.

Day 5 Streymnes, Streymoy, Faroe Islands

Day 6 Lerwick, Shetland Islands, Scotland

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.

Day 7 Portree, Isle of Skye, Scotland

The Isle of Skye ranks near the top of most visitors' priority lists: the romance of Prince Charles Edward Stuart, known as Bonnie Prince Charlie, combined with the misty Cuillin Hills and their proximity to the mainland all contribute to its popularity. Today Skye remains mysterious and mountainous, an island of sunsets that linger brilliantly until late at night and of beautiful, soft mists. Much photographed are the really old crofts, one or two of which are still inhabited, with their thick stone walls and thatch roofs. Orientation on Skye is easy: follow the only roads around the loops on the northern part of the island and enjoy the road running the length of the Sleat Peninsula in southern Skye, taking the loop roads that exit to the north and south as you please. There are some stretches of single-lane road, but none poses a problem.

Day 9 Dublin, Ireland

Dublin is making a comeback. The decade-long "Celtic Tiger" boom era was quickly followed by the Great Recession, but The Recovery has finally taken a precarious hold. For visitors, this newer and wiser Dublin has become one of western Europe's most popular and delightful urban destinations. Whether or not you're out to enjoy the old or new Dublin, you'll find it a colossally entertaining city, all the more astonishing considering its intimate size.It is ironic and telling that James Joyce chose Dublin as the setting for his famous Ulysses, Dubliners, and A Portrait of the Artist as a Young Man because it was a "center of paralysis" where nothing much ever changed. Which only proves that even the greats get it wrong sometimes. Indeed, if Joyce were to return to his once-genteel hometown today—disappointed with the city's provincial outlook, he left it in 1902 at the age of 20—and take a quasi-Homeric odyssey through the city (as he so famously does in Ulysses), would he even recognize Dublin as his "Dear Dirty Dumpling, foostherfather of fingalls and dotthergills"?For instance, what would he make of Temple Bar—the city's erstwhile down-at-the-heels neighborhood, now crammed with cafés and trendy hotels and suffused with a nonstop, international-party atmosphere? Or the simple sophistication of the open-air restaurants of the tiny Italian Quarter (named Quartier Bloom after his own creation), complete with sultry tango lessons? Or of the hot–cool Irishness, where every aspect of Celtic culture results in sold-out theaters, from Once, the cult indie movie and Broadway hit, to Riverdance, the old Irish mass-jig recast as a Las Vegas extravaganza? Plus, the resurrected Joyce might be stirred by the songs of Hozier, fired up by the sultry acting of Michael Fassbender, and moved by the award-winning novels of Colum McCann. As for Ireland's capital, it's packed with elegant shops and hotels, theaters, galleries, coffeehouses, and a stunning variety of new, creative little restaurants can be found on almost every street in Dublin, transforming the provincial city that suffocated Joyce into a place almost as cosmopolitan as the Paris to which he fled. And the locals are a hell of a lot more fun! Now that the economy has finally turned a corner, Dublin citizens can cast a cool eye over the last 20 crazy years. Some argue that the boomtown transformation of their heretofore-tranquil city has permanently affected its spirit and character. These skeptics (skepticism long being a favorite pastime in the capital city) await the outcome of "Dublin: The Sequel," and their greatest fear is the possibility that the tattered old lady on the Liffey has become a little less unique, a little more like everywhere else.Oh ye of little faith: the rare ole gem that is Dublin is far from buried. The fundamentals—the Georgian elegance of Merrion Square, the Norman drama of Christ Church Cathedral, the foamy pint at an atmospheric pub—are still on hand to gratify. Most of all, there are the locals themselves: the nod and grin when you catch their eye on the street, the eagerness to hear half your life story before they tell you all of theirs, and their paradoxically dark but warm sense of humor. It's expected that 2016 will be an extra-special year in the capital, as centenary celebrations of the fateful 1916 Easter Rising will dominate much of the cultural calendar.