Bergen is the second largest city in Norway and known for the colourful harbour and (unfortunately) the rain. From here there are great trips to Voss and Flam.
The capital of Norway is a busy place, compared to the rest of Norway, but relaxed compared to many world cities. Tourists may like the Aker Brygge harbour with its many restaurants, the Vigeland park with its many naked statues and possibly the huge Holmenkollen ski jump.
Alesund is a beatiful, but touristy little city on the Atlantic coast.
Hammerfest claims to be the most Northern "city" in the world. It is also close to the North Cape. In winter you wont have much light, in summer the sun shines all day long.
The Lofoten is a group of picturesque islands in Northern Norway. You can see fishermen´s villages, rock formations and birdlife from up close. Beautiful, especially when you are lucky with the weather...
The most Northern point of Europe has a large metal globe as a proof. In summer it is memorable to stand here in the middle of the night and watch how sunset and sunrise merge over the Nordic sea, without the sun ever disappearing.
Stavanger is a "major" city in Southwest Norway near several fjords. A very popular day trek is to climb Preikestolen (~ Preachers Chair) with magnificent views straight down an extremely steep cliff.
Trondheim is the 3rd largest city in Norway dating back to the times of the Vikings.