There would be a lot of car time. Not sure the 8 year old would enjoy that much time in a car. It is a 2+ hour ride to the west end of the island depending on traffic.
El Yunque is a fairly easy drive, however the resort I talked about can only be approached from the south side since the bridge washed out 3 or 4 years ago. There are plenty of places in El Yunque closer to SJ than the one I referenced.
I think if I was traveling with an 8 yr old I think the rain forest would be my primary goal and then wait for the calmer waters of STJ to enjoy the sea.
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