You'd probably have to fly by way of Oslo, but once you are there, it is easy enough.
Several outfits do whale watching tours in anything from small open boats to luxury cruises.
It is, however in the middle of the dark season, since the Herring hangs around november-december, so there is not much daylight.
On the other hand, that gives an excellent chance for aurora borealis.
We sailed up there with Hurtigruten in October and had a fine display.
Actually, if you want to do it the best way, going either up from Bergen to Kirkenes or the other way round with hurtigruten is something I can recommend.
I gave my wife the trip for her 60 birthday ( And joined her, of course) and we have decided to do it again when she turns 70.
Lots and lots of Orcas and Humpbacks: