On the surface, Iceland offers some of the same Far North attractions for which Alaska is well known, including a robust northern lights-viewing trade in the winter. But it's the differences that make Iceland an interesting stop.
Most travelers, when visiting Iceland for the first time, stick close to the capital city of Reykjavik. That's not a bad strategy -- it's a friendly town. Your airport bus (they sell the tickets on board the Icelandair flights) will take you to your hotel or guesthouse. From there, you can catch any number of excursions, including the famous "Golden Circle" tour, which includes a visit to Iceland's own "rift valley" where you can see the tectonic plates pulling apart the earth. The site is a national park "Thingvellir"---where Iceland's general assembly first convened in the 10th century. The Golden Circle tour also includes stops to see the incredible waterfall at Gullfoss and the oh-so-active Geysir, whcih shoots steaming water in the air every five to eight minutes.
Icelandair offers a free stop in either direction when traveling from Anchorage to Europe. Tip: take the stop. The flight from Anchorage to Reykjavik is a little more than seven hours. From Keflavik International Airport (about 40 kilometers from Reykjavik), you can connect to 13 European countries.