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Northern Lights tours with a campfire dinner with MREs, roasting sausages and marshmallows. Depending on the conditions you may go over the border into Finland.
Vår Frue Kirke
This tiny church is the seat of the world's northernmost Catholic bishop, and also dates from 1861.
University Museum
A rather large museum with a number of different exhibits on the North. Look out for their Sami exhibits, the Archaeological Exhibit, Religious art and Northern Lights machine. Avoid Sundays, as weekend daddies let their little monsters run screaming through the exhibits.
Polarmuseet i Tromsø
The museum is housed in an old warehouse from 1830 and displays Arctic hunting from Tromsø and expeditions to the Arctic. A guidebook is provided for English and other languages, though many of the displays are in Norwegian, so you'll need a translation app to read them such as Google Translate.
A preserved seal hunting vessel, right next door to Polaria. Combined entry with Polarmuseet, Tromsø University Museum or Polaria available.
Has temporary exhibits on the North. Their location in an 1838 building in the main street is superb, and there is free admission.
Nordnorsk Kunstmuseum
Has art from Northern Norway from 1800 onwards, and Norwegian art in general. Look out for their temporary exhibits.