I guess you mean Tromsø; Troms is a huge state in Norway :-)
Basically you have two areas for your journey:
A1) Norhern Fjord Norway: Ålesund , Geirangerfjord
A2) Southern Fjord Norway: Bergen, Sognefjord (incl. Flam)
B) Arctic Circle for Northern Lights: Lofoten and Tromsø.
Northern Lights (NL) means travel dates September to March above Arctic Circle. For length of daylight and weather conditions Sept and Oct. are good. You will need a clear sky and the appearance of NL - at least question of luck. Both cannot be forecasted, so you need to stay for 4-5 nights and hope for your luck. Every night more is one more chance. Travel dates around new moon would help you to see even weaker NL. A rental car will help to get to nice places but also to drive 100 km or so if the weather there might be better. For Lofoten either fly to small airports EVE or LKN and rent a car there. Tromsø has its own airport TOS.
Because of looong distances between A) and B) you need to fly or take a Hurtigruten ship (port-to-port) which takes 2-3 days but is a real nice experience.
Questions before further ideas:
- Are you open for renting a car? Or do you want to stay on public transport which reduces options?
- How much is budget limited?
- Does anyone have sea sickness?