The northern terminus of the Norwegian railway, Bodo, Norway, is slightly north of the Arctic Circle (watch for the marker just before the train pulls into town) and 525 mi/845 km north of Oslo.
There's not much to do in Bodo, although the modern cathedral is interesting, and the Norwegian Aviation Museum is worth a look (http://www.luftfart.museum.no). Nonetheless, the train trip there is a good way for Eurail pass holders to see a bit of tundra.
Bodo is also very popular in summer—it's one of the largest towns in Norway that experiences the midnight sun (approximately 6 June-8 July). It also has a completely dark winter, should you want to get a taste of that.
You can use Bodo as a jumping-off place for trips to the Lofoten Islands or for visiting the nearby Svartisen Glacier (excursions available on summer weekends only). http://www.visitbodo.com.
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