For sightseeing in San Juan, I recommend walking through Old San Juan (uphill) to Castillio San Cristobal. You can see it from the port and it's only about a 10 minute walk. It is a 500 year old Spanish fort that is now an official National Park Service site. It must be the highest ground in San Juan and the views are fantastic in every direction. Also, it has been beautifuly preserved and contains many historical artifacts.
When your done, visit the restaurant where the pina colada was invented! I don't remember the name, but any local can tell you where it is.