We have stayed on Puerto Rico twice on our way to other islands. Things we did –

Wandered around Old San Juan. We stumbled into a tour of the governer’s mansion, which was very interesting.

Both forts. You could do both in a day.

Private rainforest tour with http://elyunque.com/islandwalkers.htm. Typically, we aren’t the type to hire private guides but holy cow, was it worth it in this case. His recommendations on timing (to avoid the crowds) and particular hikes were valuable and certainly enhanced our experience. He picked us up at the hotel and returned us afterwards. He was a very informative, interesting guide.

Lunch at liquido beach (based on the above guides recommendations)

Fajardo bio bay tour. We did the electric boat tour and that was a good choice for us.