Here is what we did with our teens--all DIY or booked online with tour company. We spent about $500 total on excursions.
Stavanger: boat tour to fjords--3 hrs long and an easy morning--right at the harbor where you dock. most were DCLers who also booked directly with the boat. under $150 for a family of 4 thru rodne.no.
Alesund: walked around town and then did the 418 step climb to the top of the mountain. Lots of 5 yr old doing it, great views, easy 1/2 day, free.
Geiranger-we did the bus to top of Mt D and also kayaking, but there is a tourist bus to 2 look out points that would be fine for a younger kids and there is also a 1 hr boat tour. For young kids, I might choose 2 stop look out shorter bus and boat tour and do something different in Stavanger (there are a few museums and the town is cute), if you do a boat tour in G. We used geirangerfjord.no for bus and kayak (DD and I did bus, DH/DS kayaked--kayaking was sold out on
DCL--this was 1/2 the price and excellent--book ASAP, as it fills up. They will pick you up for free at the very small port--just ask).
Bergen, go off boat and walked around (raining). We went to Hanseatic Museum and then took the included shuttle to the Fishing museum, which would be excellent for kids-teens. We also had online tickets to take the funicular to the top of the mtn, but it was raining, so we skipped that. It was worth it to buy tickets online to skip the crowds, even though we didn't use them. We got one way--about $30 for family of 4. Having now been and talking to others on DCL, I would not change any of above. Perfect mix of cost-effective sightseeing and active stuff.
We LOVED the fjords cruise--great mix of ports, scenery and plenty of time to do all the fun DCL stuff. My 2 teens watched 7 movies that week-not b/c they were bored, but b/c of the easy availability (Mom did not have to drive them).