For beaches, go to the Condado and walk through the hotel but avoid having anything on you that marks you to a cruise line and walk out the other side on to the beach.
You can also take a taxi to Isla Verde which is about five miles farther east and there are lots of hotels with good beaches. Keep in mind these are Atlantic waters so the sand can be kind of "dirty."
There are probably excursions that will take you to Luquillo beach in Fajardo which is quite a bit farther east past the Intl. airport.
If you do the Bacardi tour, taxi from there to Dorado beach and go to the Dorado Del Mar or the Cerro Mar hotels.
Be careful with public beaches where you can be robbed blind. Not to scare anyone but the crime in PR
has accelerated by 800% in 10 years. (I did not add any extra zeros.)
To be safe, stay in the Condado, Isla Verde or go on the excursions and private beaches.
As for the Bacardi tour, you can really get your fill there and purchase some to be held until you disembark. Be sure and try 151 proof but don't light up at the moment. My experience has been that the ships shops tend to have excellent deals on liquor. I'm talking Jameson for $12.00 and Crown Royal for $ 10.00 so watch for the deals on board too.
Whatever you do in San Juan:
-Do not go to La Perla, a small village of shacks below the cemetary by fort of El Morro.
-Do visit the restaurant, "El Meson" and have a Cubano sandwich. It is like Puerto Rican fast-food but really well done. The crab sandwich would be excellent too!
Have a great time in PR