The islands are very different, it really depends on what you want, but with 2 teens I would just go to Honolulu, as they other islands are pretty quiet. I have not taken my girls yet, but I think the first time we all go, it will be Honolulu for a week, and then Maui.
I know a lot of people say Honolulu is a just another big city, but I like it, the beaches are beautiful, climbing Diamond head is fun, and if you like, you do not need to rent a car. First time we went, we rented bikes and you can take your bikes on the public buses, so we would take the bikes on the bus to other parts of the islands and then spend the day, we found some wonderful beaches and got off the busy areas, when we were tired of the bustle.
The other islands are special too, but everything is more spread out so you do lots of driving, and have a much more layed back attitude.
I have been to the Big island also and seeing the volcanco at night is something I will never forget.
Kaui is my favorite(without kids) as it is so beautiful, beches were not as nice, but it could have just been the time of year we were there (December) and the waves were rough.
Maui, the dive to Hana is not to be missed.