The Cuartel Moncada is where the Cuban Revolution began. Now a primary school and museum, the building still shows the bullet holes from Fidel Castro's 1953 attack (though some say they were filled in by Batista and re-drilled after the revolution for authenticity). The Museo 26 de Julio inside gives a vivid and unsentimental account of the attack, the rebels' capture, and the subsequent trial at which Castro made his famous "History will absolve me" speech.
Whatever you think of the politics, the museum is honest about how badly the assault went and how high the cost was — the photographs are not sanitised. The building is a short walk north of the Parque Céspedes. Entry is cheap and a guided tour in Spanish is usually available; some English-speaking guides can be arranged.