Background: The aim of this preliminary study was to measure radon concentrations in a hospital in order to verify to what extent these concentrations depend on various environmental variables taken into consideration, and consequently to determine the urgency to implement mitigation actions. Methods: The rooms where the concentration of the gas was potentially highest were monitored. Investigators adopted a Continuous Radon Monitor testing device. Qualitative and normally distributed quantitative variables were summarised with absolute (relative) frequencies and means (standard deviations, SD), respectively. As regards environmental variables, the difference in radon concentrations was determined using the rank-based nonparametric Kruskal–Wallis H test and the Mann–Whitney U test. Results: All measurements, excluding the radiotherapy bunkers that showed high values due to irradiation of radiotherapy instruments, showed low radon levels, although there is currently no known safe level of radon exposure. In addition, high variability in radon concentration was found linked to various environmental and behavioural characteristics. Conclusions: The results on the variability of radon levels in hospital buildings highlighted the key role of monitoring activities on indoor air quality and, consequently, on the occupants’ health.