We were 2 families with a total of 4 kids ranging from 3 years old to 9 years old. We took the ferry to Red Hook, got a car rental "shuttle" to the Avis place and rented a van big enough for all of us. We drove to Cinnamon Bay, which is just past Trunk Bay and much quieter and less crowded. Just remember that they drive on the left! You can even rent snorkeling equipment at Cinnamon Bay. There was hardly anyone there and the beach was very nice - snorkeling was pretty good, too. I don't remember exactly how much it cost, but it was not too expensive even for all of us. I think the van cost $50 to rent. If you didn't have that many people it might be just as cheap to take a taxi. If you go to Cinnamon Bay, I would suggest asking the taxi driver to pick you back up at a certain time, though - it is not like Trunk Bay where there are lots of them waiting to pick you up.
Oh - Cinnamon Bay also has an outdoor restaurant, although I'm not sure of the hours (it was closed when we were there), and they also have a little "campground" type store with snacks, drinks, etc.