Presuming you're embarking from San Juan, then Old San Juan is the obvious suggestion. You can spend the better part of a day or more just wandering around. It's very much like an old European city.
You should definitely check out El Morro, a large fort overlooking San Juan Bay. There's also a Bacardi rum factory just west of El Morro that allegedly gives tours.
Do you like beaches? San Juan has plenty, although I didn't find them spectacular.
If you have at least half a day to kill, drive an hour or so east of San Juan to visit the El Yunque rain forest.
Old San Juan is pretty cool. Nightlife there isn't bad. El Yunque is a day trip (45 minute drive from San Juan) and is a good place to hike and expereince a rain forrest. If you had more time I would strongly suggest Culebra or Vieques... The caves and the arecibo observatory are over rated. The bacardi factory is quick and easy. You pay a couple dollars to take the ferry across the bay and when you get to the other side there will be a dozen taxis waiting to drive you the 5 or 6 blocks the the facaility where you get free booze...