There will be many divided opinions here as lots of people have their own preference. Mine is for Trellis Bay, for which I will probably get some flack. It is a quiet, secure mooring field (don't get caught on the reef at the Trellis end of Bellamy Cay, aka Last Resort) . I frequently swim in the water, which although it is not teaming with fish life due to the frequency of various ferries etc, is clean. I have never had a stomach upset and there are frequently turtles and even dolphin. The clarity of the water is generally excellent. It is close to the 'village' of Trellis Bay and da la Mongoose has good food and drinks, as does Last Resort, either of which your kids will enjoy. So convenient for the airport without a long dinghy ride or relying on a ferry.
As I say, others will chime in and certainly suggest Scrub. If you like that sort of thing, fine. I don't come to BVI for that type of place/experience, but each to their own.