Along with the National Theatre, the Costa Rican post office is one of the city's main historical moments, and is worth a look. It has beautiful architecture dating back to 1917, and offers some lovely views.
About two blocks away from the Plaza de la Cultura, and in the Morazon Park, this is a particularly beautiful and impressive place to visit. The rounded dome, dating back to the year 1920, is particularly charming. Don't miss it.
The National Culture Centre includes several cultural and ministerial institutions like the Ministry of Youth and Sports, and is totally open to the public. I love the remarkable Costa Rican architecture.