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 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.
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.
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.
Flåm is known for a trip called "Norway in a Nutshell", consisting of train and ferry rides.
The Geiranger Fjord is famous thanks to its natural beauty and the many waterfalls. The best views can be had from Geiranger village. It is UNESCO heritage and featured on most post cards.
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.