Norway has an incredible variety of climbing, from fjord-side sport crags to polar alpine epics. The highlight of alpine climbing in the country is an ascent of its "national" mountain, Stetinden. The standard route weighs in at YDS 5.6, while the enticing South Pillar Route tallies in ~5.9. The Lofoten Islands are a popular climber's destination, and offer everything from hard bouldering to long alpine routes. Climbing potential exists at almost every turn in Norway, so don't despair if your journey doesn't take you to one of these locales. Drop by the local outdoor sports store and look for a partner and information. Great climbing can be had close to almost every major city, including Bergen & Oslo. Keep in mind that the weather plays a significant role in Norwegian climbing. It will rain at some time during your stay, if not the whole time. Norwegian climbers take a philosophical view of rain, classifying showers in two types: those wherein you can still climb, and the ones that are too drenching to climb in! Not all cliffs are "good" for climbing, though in Norway, very little doesn't get climbed regardless. The infamous Troll Wall for example, is a 5000' high chosspile, but it is also one of the most sought-after faces on the planet.
By air from the New World; by train, ferry, or auto from Europe. While public transport excels in Norway, the backwaters have very limited schedules. Travel to Stetinden, for instance, is possible via public transport, but if your travel time is limited, consider renting a car.
Mountain Project's determination of some of the classic, most popular, highest rated routes for Norway: