I have been to Old San Juan numerous times. I don't consider it a beach destination. Although you could visit some of the beach front hotels in Condado and Isla Verde, which are just a taxi ride from OSJ.

At one point the El Convento Hotel had a sister hotel in Condado which you could visit. I think some visitors to Puerto Rico go to Playa Luguillo, but I have never been a fan, and you would probably need a rental car.

I think the best beaches are on the west coast of Puerto Rico, in Aquadilla and Rincon.

You will definitely love Old San Juan though. Lots of history and great restaurants!