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Ancient monuments located in urbanized areas are subject to numerous short- and long-term environmental hazards with flooding being among the most critical ones. Flood hazards in the complex urban environment are subject to large spatial and temporal variability and, thus, require location-specific risk assessment and mitigation. We devise a methodological scheme for assessing flood hazard in urban areas, at the monument's scale, by directly routing rainfall events over a fine-resolution digital terrain model at the region of interest. This is achieved using an open-source 2D hydraulic modelling software under unsteady flow conditions, employing a scheme known as 'direct rainfall modelling' or 'rain-on-grid'. The method allows for the realistic representation of buildings and, thus, is appropriate for detailed storm-induced (pluvial) flood modelling in urbanized regions, within which a major stream is usually not present and conventional hydrological methodologies do not apply. As a case study, we perform a pilot assessment of the flood hazard in the Roman Agora, a major archaeological site of Greece located in the center of Athens. The scheme is incorporated within an intelligent decision-support system for the protection of monumental structures (ARCHYTAS), allowing for a fast and informative assessment of the flood risk within the monument's region for different scenarios that account for rainfall's return period and duration as well as uncertainty in antecedent wetness conditions. [ABSTRACT FROM AUTHOR]