Absolutely a must when in San Juan: to tour the Castillo San Felipe de Morro and Castillo San Cristobal Forts which make up The San Juan National HIstoric Site. These two historic sites are a part of the U.S. National Parks System and as a result, preserved so well with excellent way-finding to tour on your own. We definitely spent a good few hours going through both the forts and it was a lot of fun exploring all the ins and outs...which included a dungeon with drawings of ships on the walls, reading about the history, and seeing great views from the top.
The forts were constructed under Ponce de Leon to help the Spanish Empire maintain its control of the Caribbean during the 1600s and 1700s when war and trade traveled on sailing ships. The architecture was an example of exemplarily military engineering at the time.
We started at Castillo San Cristobal, and since it was incredibly hot, so we hopped the free tourist shuttle to take us to El Morro. When at El Morro, be sure to peek at the cemetery east of the site.