Grouchy Imp said:
I regularly go to Tromsø for two things: shopping Magic: The Gathering and eating the best steak in Norway. Skarven [http://www.skarven.no/] is the place, and they also have other meals that are very palatable, especially fish based ones. If you go there I'd recommend getting reservations a week in advance, it's popular. It's definitely one of the more expensive places to eat in Tromsø though... And that says a lot for a country that has a high cost of life. If you would like to spare as much as possible "wallet impact", I would recommend Steakers. Just ask for Steakers in the reception where you'll be staying and it shouldn't be hard getting directions.
Anyway, if you are seriously planning a trip to Tromsø, I absolutely must recommend you make a day or two's trip to Lofoten, especially if Northern Lights are the attraction:
Tromsø is connected to Svolvær with hurtigbåt (fast boat, like a bus on the water

)
In Lofoten, it's much easier to escape light pollution and get a fantastic view, and in addition, the landscape is breathtaking. An added bonus is the sea horizon, that lets a thin sliver of light be seen during the winter at noon.
But yeah, hope you have a great time no matter what.