With only 8 days you would be pushing it to get up to Bay of Islands - it is a couple of hours past Auckland so you would lose a day just getting there and back.
I would agree with this also really depends on weather, so you might want to have options for good bad weather. We did bay of islands but weather was lousy and was alot of travel for not much return in that weather. We did do sand boarding in 90 mile beach (in the rain - and had a dodgy neck for a few days after a head meets sand very fast incident ;-)).

Depends what your boys are into - I got alot more from the boiling mud, geysers volcanic activity stuff (Rotorua Taupo etc) than the beach type stuff (Cathedral Cove etc ) my inside 8-9 year old self loved volcanic/earthquake stuff and that would be the stuff I would look forward to taking my kids to. Hot water Beach was fun but I wouldn't prioritse it.

I saw lots of kids doing the Tongariro crossing the Blue lakes, views and rock scrambles fun, but is a long walk (all day) so depends what your two like. Most of the kids were putting me to shame.

If you look up Magic Bus that has several routes round the North Island and to break up journey had lots of fun stopping points. It may help with timings etc.