You can always take a walk around Old San Juan and visit the old fort "El MOrro", its a nice walk and some nice shops along the way. The view from up there is something else, worth seeing :-)
I spent a week in San Juan last November and wish I had booked a shorter trip. First, it's not exactly exotic, since it is a US territory and very americanized. El Morro and Old San Juan (where you will dock) are worth a walk/look. You can also take a taxi ($6) to the Condado area, for restaurants and more mainstream shopping or if you need to find a real store like Walgreens or something. The food is generally good...there was an Italian restaurant right at the beginning of the main drag of the Condado that was exceptional and could rival my Italian mother.
Don't bother with the rain forest. Hot, humid, no interesting vegetation, animals or even birds...just biting insects. Awful.
Just a note - the ships don't all dock "downtown". If you're at what they call the airport dock then you will have to find transportation into town - when we were there on embarkation day it was not a problem since there were lots of people arriving at the docks.
I truly enjoyed El Morro Fortress - really beautiful scenery and you can see the other fortress from there as well. Old San Juan was quaint and interesting, but the horrendous traffic and the crowds can be wearing.
I've heard some good comments about the El Yunque Rain Forest, but did not go ourselves.
Crab, Crab, Crab. San Juan is a beautiful city filled witth very nice people. We took a tour on Good Friday of last year and had a great time. We went to the rain forest and to a beach. Part of visiting other areas is enjoying the people, the customs and most of all the food. I think we had a great time. Yes, I undestand that a rain forest can be "boring". What do you expect? Neon lights??? Enjoy the country, observe how others live. The time spent a the beach was mostly enjoying the local food. Guess what. No McDonalds there. Just local folks enjoying a day off. Go, tour the Old City, visit the forts, enjoy the people and their life style.