Capt. Jay has posted his recs which are wonderful.

Are you looking for the most child friendly beaches, restaurants, activities?

Restaurants: if taking the dinghy in from Lind Point/Honeymoon, first on the family friendly list would most likely be Banana Deck. It gets gets consistently good ratings from families. There is a lot of great info on the St. John TripAdvisor forum in regards to restaurants (especially family friendly establishments).

Lime Out/Coral Bay is problematic. No public moorings, anchoring only in (typically) tight quarters. We always skip it when land or water based. You can grab a mooring (day use only) in Hurricane Hole, but it is a long dinghy ride into Coral Bay to visit Skinny Legs, etc.

Beaches: Francis and Maho have consistently calm water and easy enrty for kids with good snorkeling. Maho has gotten incredibly busy due to Maho Crossroads but still holds appeal in the early morning and late afternoon when the land based beach goers head back to their rentals. Honeymoon has concessions but it too has gotten very busy and has developed a party atmosphere. Grab a mooring at Cinnamon and take the Cinnamon Bay Trail or a ball at Trunk and snorkel the underwater trail by the Cay. Pizza Pi in Christmas Cove (STT) is always fun for kids of all ages.

Have fun!