We're just back from Bergen.
There is LOADS of really good walking to be done at the top of the funnicular. Proper walking trails - you could walk for miles, if that's your thing (we hadn't realised it was so extensive, so didn't really have the right footwear on). You can go on a canoe on the lake up there free - it's not a big lake, but people were having fun doing it.
If you/your teen are into football, there's an exhibition on at the Bryggen museum about the local team. We didn't have time to see it as we spent a long time in the main bit of the museum (which is well worth a look).
The Nordnes area of town was lovely to wander around. Really beautiful tiny streets. The aquarium is there, which is apparently good. There's also a 'beach' there - if the weather is good, take your swimmers. So many people were swimming in the sea/fjord and just chilling by the shore.
Even though you're going to the fjords, you may well want to do a boat trip from Bergen too. That seems to be the main kind of 'activity' on offer in town (we mainly mooched around, enjoyed the weather, stopped for ice-cream/beer, and visited a few places with our Bergen cards).
The Norway in a Nutshell tour is really popular - we didn't do it as we'd already done the train from Oslo as far as Flam, and then did the Flam railway from Myrdal.
It is a beautiful city - and the light nights are really special. Hope you get good weather like we did.