Yep.... rain forest and the forts. Old San Juan is makes for a nice walking tour being as much Mediterranean as Caribbean. it has city walls and historic squares. If one's into history then they can't help but love San Juan.
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Like Trip said, it all depends on what time you get into port. San Juan is the capital of Pueto Rico, has the busiest ocean terminal in the West Indies and is one of the cruise trade's most important ports. Old San Juan is the primary spot for cruise passengers because the docks are right at its foot. You really don't need to bother with an organized tour of Old San Juan just pick up a street map and go it alone. The two Forts, El Morro and San Critobal are both within walking distance of the pier and managed by the U.S National Park Service. Admission is about $5. and is good for both. Guided tours are also available.
The Bacardi Rum Distillery is also worth a visit. But you will need a cab to get you there and it can be a bit pricey.
In June, my wife and I went to El Yunque Rainforest (via a shore excursion through Carnival) and we both really enjoyed it.
You can also go to the casino in the Sheraton Hotel which is direcly across from the pier.
Note: liquor prices are even lower here than in St. Thomas and US citizens do not pay duty.