Hi Janey! :)
First off, you will love Tromso! It is an absolutely gorgeous city so you won't be disappointed there...
The only downside for me to Tromso is that it is more likely to be covered in clouds than areas further inland due to the Gulf Stream influence.
My suggestion is to either rent a car and drive inland if this happens (in any case you will want to get away from the light pollution from Tromso) along the E8 road, can't get lost really only 1 main road. The problem with stayin in Tromso is that the Aurora can appear at anytime, and staying in the city really limits your chances of seeing the lights properly unless you are prepared to drive at a moments notice outside the city. So if you want the do it yourself option, be prepared to find a good spot long the E8 and wait it out =)
A tour guide will really give you the best chances as they know the local area well, one in particular Kjetil Skogli will drive for hours in search of clear skies and Aurora if the activity is there. Here is his site - http://www.kskogli.no/aurora/ You will literally be under dark skies for hours on end, as good a chance as any to see the lights.
I've written an article all about the lights, perhaps you'll find this helpful too http://www.natalia-robba.com/myblog/travel/the-aurora-borealis-the-northern-lights-everything-you-need-to-know/
Natalia