Your adventure begins in Reykjavik, the world's most northerly capital city, which is home to around a third of Iceland's population. The city boasts a cultural and culinary scene that belies its diminutive size, and is home to head-turning architecture such as the concrete Hallgrímskirkja church and the shimmering Harpa concert hall.
It's worth spending a night or two in Reykjavik before or after your cruise; not only to explore the city, but also to venture out into the surrounding countryside and tour the 'Golden Circle'. This circuit links together three of southwest Iceland's most famous sights: the rainbow-misted Gulfoss waterfall, the spectacular Strokkur geyser and Thingvellir National Park, site of the world's first parliament in 930 AD. The southwest of the island is also where you'll find the popular Blue Lagoon, where you can bathe in steaming geothermal waters.
Sailing clockwise around Iceland from Reykjavik, you soon arrive at the Snæfellsnes Peninsula, accessed via Grundarfjörður or Stykkishólmur. The distinctively shaped Kirkjufell mountain is said to be Iceland's most photographed spot, while Snæfellsjökull National Park is home to lava fields, bird sanctuaries and a volcano capped by a 700,000-year-old glacier.
The wild Westfjords region, which extends out from Iceland's northwest corner like a many-fingered hand, is likely to be one of the highlights of your journey. Remote and sparsely populated, the Westfjords is where you'll find the thundering Dynjandi waterfalls and the towering bird cliffs of Látrabjarg. A staggering number of sea birds nest here during the summer months, including puffins, razorbills, guillemots, cormorants, fulmars and kittiwakes. The key port in the Westfjords is Ísafjörður, though you may also see itineraries calling at Patreksfjörður and Bolungarvík.
From the Westfjords your next stop may be the little fishing port of Siglufjörður, known for its folk music and its herring museum (!), or your ship may head straight for Akureyri, the main port on the north coast and Iceland's 'second city' (albeit with a population of just 18,000). There are some cool cafés and galleries here, but most visitors will use the town as a base to explore nearby Lake Mývatn. This shallow lake is rich in birdlife, while the surrounding area is an otherworldly landscape of bubbling mudpots, bizarre lava formations and steaming fumaroles. Other highlights of the north coast include Husavík, Iceland's whale watching capital, and the tiny island of Grímsey, a weather-beaten place where humans are far outnumbered by seabirds.
Relatively few tourists make it as far as the Eastfjords, a mountainous region where quaint fishing villages are sheltered by dramatic fjords. The arty town of Seyðisfjörður, with its brightly coloured wooden houses and picturesque setting, is a highlight, and Djúpivogur is the departure point for boat trips across to Papey island, where you'll find puffins galore and Iceland's oldest wooden church. The Eastfjords is a great region for hiking, and it's also the only place in the country where you can see herds of wild reindeer.
By now we've almost come full circle, but there's just time for one final highlight. Sometimes known as 'Iceland's Pompeii', Heimaey is the largest of the Westman Islands, just off the south west coast. In 1973 Heimaey made headlines around the world when the Eldfell volcano erupted and lava began to flow towards the town of Vestmannaeyjar, threatening to engulf the harbour on which the islanders depend.
The locals were evacuated by fishing boat and half the town was buried, but firefighters were able to stem the lava flow using water pumped from the sea, and most of Heimaey's inhabitants eventually returned. Don't miss the fascinating Eldheimar museum, which has been built around the preserved remains of one of the homes buried by the ash.