Bergen is (at least from my point of view) one of the most charming cities of norway. Although it's supposed to rain all the time, it has some nice attractions to offer like Troldhaugen, Oldtown Brygge and a view from the mountain Floyen.
Absolutely overcrowed but nevertheless a must see is the house of world famous norwegian composer Edvard Grieg (1843-1907). This is the place where he composed many of his masterpieces. Take the very informative stroll through the living house, down to the composers hut at the seaside and into the little museum.
Brygge at the seaside of Bergen is the oldest district of the town. It's from the times where Bergen belonged to the "Hanse", a large and powerful trading organisation which existed up to the 17th century. You'll get a good impression on how people lived at that time.
Last but not least, a view from the mountain Floyen gives you a good overall impression of Bergen, which is nicely situated at the atlantic ocean. Floyen is easily reached from the citycenter by either hiking it up or taking the small tram. There is also a restaurant on top.