There isn't so much things to do in town in february. For sunrise/sunsets times check
this out.
It is really hard to know what to recommend without knowing your preferences. If you're into art and culture there is some nice places. The art museum has the worlds largest collection of nordic art. Hasselblad centre has a lot of stuff by extremely competent photographers. There is a vast host of independent gallerys.
If you don't fancy that kind of stuff, but more manly/boyish stuff such as technology and the like there is a cool nautical museum, a ship museum ( a lot of ships lumped together so you can go into everyone, I think they still have a sub lying around there), volvo has their own museum, there is supposed to be a radio museum somewhere, haven't seen it though. One of the garnisons has a museum too.
If you like historical sites or architecture there some stuff to do as well. A lot of historical tours start from the Gusta Adolf square. There is a couple of different forts around, some are nice, most are not. The nicest one being 80 km south og GBG, the second nicest being some 20 km north. Then there is countless semi-sites with really uninteresting historical facts.
Give us a run down of what you like and I'll see what I can come up with.
OR we could just go out and do some ice-fishing (if the weather is up for it..)