Definitely go to Old San Juan and the Forts which is in the same area, you can spend an entire day in old san juan exploring, lots of great places. The beaches in san juan are pretty decent considering it is a big city, but the boat trip you taking should take you to some nicer ones like out to vieques. Definitely go to the rain forest, join a hiking tour, they'll take you through waterfalls and zip lining.
Go to a mercado (market) where people buy their fruits and veges and you can score some cheap grubs there. There's also a really vibrant night life in PR, like old san juan, candado district has good stuff too. People there are nice and friendly.