About hiking, which Slhoka mentioned, and which Norway is really perfect for.
I'm quite into that stuff nowdays, after doing it for a whole school-year. It would be cool to arrange something the days fore or after. But know this, Norway is a spread country with diverse nature, though people goes hiking everywhere. Norway is most known for the fjords and mountains of western Norway, while we(most smashers) live in east, "the lowlands". Though it's nice here also(and it's not THAT long to the large mountain ranges), with cultural stuff to see, and some smaller mountains up to 700 moh right nearby in Eidsvoll, which Tonberry knows better, good trips and view from there it seems.
It's up to the interest, what you wish, time and sportyness really, the limits are endless otherwise. If you have a car and gas money, you can drive and see lot's of places. If you're really sporty you can go in the mountains and sleep in a tent, or in the network of huts.($) At least with car(s) we could arrange a longer day-trip to Gaustatoppen (1883m), which they say you can view 1/6 of Norway's land mass on a clear day. That's more than Denmark. =p