There are 2 great suggestions from native Norwegians and I would strongly recommend that you do more research based on their postings.
A couple of tips from me, based on my experience as a Brit in Norway.
1 Don't try to cover too much ground in one day. The roads are great for driving, but have low speed limits, and the spectacular scenery merits many stops (if only to take photos) so overall progress will be much slower than US.
2 As a result of the above I would draw up your itinerary based on your starting point. If you are starting in Oslo then don't try aiming for anything north of Trondheim.
3 The train journey from Oslo to Bergen is a certainly great way to see the country, and Bergen is a great port city to explore. From here my favourite car journey is to go across country to Voss, over to the Sognefjord, then take the E55 over the summit and down to Otta and the Sjoa valley. You can then drive north over Dovrefjell to Opdal and Trondheim. This is another city which is well worth exploring. If you are tired of driving you can take the train back to Oslo, or if not make your way back either via the Atlantic road to Molde and down through the Fjord country or the much quieter Osterdalen route.
4 Lastly Norway is not a cheap country (but don't let that put you off , it is well worth it) , it has the highest priced fuel in Europe, and alcohol is really eye-wateringly expensive, so take as much duty-free as you are allowed if you enjoy a tipple in the evenings after the driving is done.
PS Don't ever think of driving after consuming one drink, the drink driving limit is very low and enforced rigidly.
