Like the Capitolio, the San Juan City Hall is open to all visitors from Monday to Friday, 8:00 am to 5:00 pm. Located on the Plaza de Armas in a beautiful building dating back to the 17th century, the Alcadia frequently showcases small art exhibits that are accessible free of charge. Visitors can walk around the building on their own, which includes a really nice inner courtyard. Also, don't miss the back of the building (on calle San Francisco), it allows you to see the different types of architecture that were used in the design of the Alcadia.
As for the Plaza de Armas, although it was designed and is still described as San Juan's main plaza, it is fairly small and there isn't that much action going on (although we did enjoy watching two little girls feed the pigeons). There is a small fountain with four figures representing the four seasons, but it wasn't running when we were there. Also, it isn't necessarily surrounded by nice-looking buildings, the way most plazas are. The San Juan City Hall is by far the most interesting building in the area.
This large and attractive building facing the Plaza de Armas initially made me think it was a church, but actually it is City Hall. Built in stages from 1604 to 1789, it resembles Madrid, Spain's City Hall. This lovely building also has tourist information available.