Alesund is a beatiful, but touristy little city on the Atlantic coast.
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.
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.
The Sognefjord is nicknamed the King of the Fjords and the largest and deepest fjord in Norway.
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.