Hmm, up the west and into Finnmark. I'm assuming you're staying the Norgee side of the border... places I would recommend. If you're staying west, take a trip into Ålesund. It's not only a lovely town (all rebuilt art deco) but it's very adventure linked - Devold sweaters come from near there. It's right next to the Sunnmøre Alps, which are absolutely wonderful. Amazing climbing to be had, or get a boat trip and sit on deck and marvel

You must not miss Innerdalen, and Dalatårnet too!
If you're really serious about climbing, the Trollheimen is not too far out of your way - but if you want flatter ground, Dovrefjell is but a little further. This is one of my favourite parts of Norway. Along with the Rondane, it provides a gorgeous mix of flatter moor with peaks - both are very wild. See if this tickles your fancy:
http://www.aaens.dk/images/dovre fjeld sep net.jpg
There's a big gap in my knowledge that stretches from Trondheim to Tromsø, but north of that I can tell you more. Tromsø is one of my favourite cities - if you have time, get a boat around the islands. I sailed with a fisherman around the area and it is breathtaking. If you're driving to Kautokeino you must be passing through Alta - a town I know very well. Small, and dominated by the dam nearby, but the people are wonderful. If ever there were a town with character, it is Alta. Spend some time soaking up their way of life - Alta fjord (used by the Germans in WWII) is also good for boating.
When you get to Kautokeino, you must go up onto the plateau. I don't need to explain - you will understand when you get there! Plenty of opportunity to mingle with the Sami, too. You will probably need to get hold of an interpreter (locally) as the Sami don't tend to learn Norwegian - seeing how much they have been influenced by modern methods it's good to see them hold on to their language fiercely. They're a funny lot - they can be a huge amount of fun and extremely generous, but occasionally something will come up that is simply very different - for example, they have no concept of chance - either something will happen or it won't.
Anyway. I've doubtless gone on too long already - if you mention what sort of areas and types of things you're interested, I might know a few places
Cheers
Chris