I have stayed on the island for many years wth my teenage boys and girl. From my perspective, I would stay on Coral Bay because a visit to St. John is a time to de-compress and enjoy family togetherness. I have found that my children have strengthened their personal relationships and as a result STJ is a special place for them. They have developed themselves pesonally by writing a journal and reading. The meals that we cooked together enabled the family to collaborate as a functioning team. Our home life was way too busy with school, sports, social activities, etc. A trip to STJ Coral Bay allowed them to just be themselves.
Evening visits to Cruz Bay were all about eating and drinking and shopping. Which of course we all love to do, if it is in the budget. There are many wonderful shops in Cruz Bay and things to buy that I simply can't afford.
So, in addition to the considerations above think about the overall vacation budget and perhaps reserve a special "dress up" night and have a lovely evening in Cruz Bay.
Last year my daughter and I took a solo trip to the island. We rented a condo in Cruz Bay because we couldn't get a car and wanted the convenience of taking taxis to th beach. We had a lovely time. However, since she was only ever exposed to Coral Bay on previous trips she mentioned that she missed the BIG Coral Bay view, the sounds of the tree frogs at night, the open space you get at a villa rental and accessibility to salt pond and the more remote beaches.
Whatever you decide to do. I can assure you that this vacation will be special and very memorable.