Cleobeach,
Puerto Rico has always been a special place for my wife and me. It was where we spent our first two years of marriage. A couple years ago we went back and just spent the week circumnavigating the island. We stayed in El Yungue for a two days and 1 night at
Casa Cubuy Eco-Lodge. Although the place is a little tired the location is absolutely amazing. Perched high on a mountain, the sounds of waterfalls and coqui frogs will put you to sleep at night. And when you arise here is your view.
The place is run by a retired School Teacher (Defense Dept) who has live in PR since the early 70s and her son. It is not a Hilton by any stretch, but if location matters and you like to hike this may be the place for you for a couple days. Just a short walk below the eco-lodge is a wonderful waterfall with a great pool for swimming after a hike.
If you do not like to be in remote places where there are zero street lights at night this is not the place for you – there is nothing there but jungle, frogs, flowers, and waterfalls. And in our case we were the only guest also.
We are also big fans of the western side of the island. The beaches of Jobos, Borinquen, Crashboat, and Rincon are a big draw for us. Albeit they can be fairly rough in the winter time many of these same beaches are great for whale watching. Rincon is also known as a world class surfing location. Unfortunately on our last visit it was during a Tropical Depression and the water was pretty churned up but this should give you view into the beaches.
The Paradores (small inns or like a BB) can provide you some out of the way places to experience also. I cannot remember the name but there was a Parador in old coffee plantation near Mayagüez that was absolutely beautiful.
Of course there is the Arecibo Observatory that may peak the interest of your 8 year old, but if you are not prone to car sickness continue on Highway 10 up to Utuado and over to Ponce on the south coast. What a ride!
There is so much more to PR once you get out of San Juan. San Juan is great big city, but it is a big city… of course IMHO.