I did a 2 week trip but did not use public transport outside of the cities. My thoughts on main destinations:
Oslo: Nice enough city, but nothing special compared to other European cities. There are a couple of interesting museums but otherwise not much history. Eating out is expensive and not particularly outstanding. I wouldn't spend more than 2 days (1 day might even be sufficient).
Bergen: A bit more history (old warehouses along the waterfront, small and interesting museums, etc). I would say it is the most unique town/city in Norway. A nice way to end your NiN trip.
Tromso: Small, can easily see what's available in a day. Many use it as a base for Northern Lights viewing (more tour agencies, infrastructure, etc) but be aware that you need to get out of town to view the lights. Most Norwegians we met suggested picking a smaller village in Lofoten or Vesteralen (or further north) and just try your luck every night instead of going "hunting". We went in the summer so it didn't really matter.
Other towns like Trondheim, Stavanger, Alesund: Can really skip, nothing special. However, Stavanger is a base for the Preikestolen (Pulpit Rock) hike, Norway's most popular, and there are many bus+ferry arrangements to get to the hiking starting point and back. There are also interesting hikes near Andalsnes. All of the above towns can be reached by bus/train.
Lofoten: The highlight of Norway and should not be missed! The main towns are Svolvaer and Leknes, but neither were as nice as some of the smaller towns and villages. Henningsvaer and Nusfjord are beautiful, but the best bet is to base yourself in Reine, in the south. Lots of organized activities, hikes, etc nearby. Indeed, Reine might also be a good base for Northern Lights; there's a very good tour operator in the village center who takes people out on RIB boats for wildlife viewing and northern lights. There are public buses (not very frequent though) that run along all the main towns of Lofoten.
https://lofoten.info/en/bus/?Article=21
Flight tickets (SAS, Norwegian and Wideroe) can be very affordable if you book early.
Norway is truly a country to be experienced rather than to be seen. I'm comparing it to places like Switzerland, where transportation infrastructure is good, and you can see beautiful sights without much effort. In Norway, on the other hand, the best sights are usually at the end of a hike! Norwegians seem to want to keep everything natural without building up too much. With the oil wealth they have, they can live like Gulf Arabs. But instead, they seem to be hardworking people living with nature.
Your initial question was if 2 weeks is too much for Norway. That really depends on your travel style. If you are a city person, then yes; you're better off adding other more interesting Scandinavian cities (Copenhagen, Stockholm) to your itinerary; after all, Oslo-Copenhagen is a lot nearer than Oslo-Tromso. But if you like hiking, nature and wilderness, then no, 2 weeks may not even be enough.