Polaria is one of my favourite attractions in Tromso and the first museum I visited in the city last year. Actually, it's not really a museum but rather an aquarium which happens to have a cinema as well. It's quite an interesting building, resembling ice floes, and it's only about 5 minutes from the city centre by foot.
At Polaria you can see all sorts of northern fish and marine mammals, like king crabs and 4 bearded seals, namely Bella, Mai San, Lyra and Loffen. There's a show with the seals twice a day (I think so at least) and even though I don't really enjoy to see these animals in captivitiy to entertain tourists, I couldn't see any signs that they were not taken care of in a humane way. Also the show is supposed to train the seals mentally so that they don't become bored and so that they feel comfortable during veterinary examinations.
Apart from that, Polaria has a panoramic cinema where you can watch a Northern Lights movie and one about Svalbard. I enjoyed them both so I can only highly recommend you to visit Polaria. They also have a lovely cafe upstairs and a gift shop that is not as tacky as others (if a gift shop can ever be not tacky at least). And the patio opposite of Polaria is the only place in the city centre where you can sit at the waterside (so naturally, it's a place I love).
I also read on their website that they have a new exhibition called "priceless" which is concerned with the melting of the ice in the Arctic. I have not seen that one yet but it sounds quite interesting so I might visit Polaria again soon. They also offer Northern Lights tours and invite you to a private screening of their Aurora movie if the lights don't make an appearance, pretty cool right?