Cultural goods refer to a broad area, sometimes difficult to isolate. Amongst other cultural sites, museums can be regarded as a bundle of cultural goods that play a relevant role as a repository of heritage roots, cultural diversity, education and able to exert several spill-over effects. However, little is still known on the determinants that affect the demand for cultural goods. Based on a microeconomic theoretical framework, the objective of this paper is to assess what factors influence the intensity of attendance to a museum. This aim is pursued by applying a quantile regression for count data models, a là Machado and Santos Silva, to cultural consumer data gathered at the end of the visit to an Italian National Archaeological Museum in 2011. On the one hand, the findings indicate that economic factors and tastes may not be the only determinants to affect demand for cultural goods, as the intrinsic characteristics of cultural sites may be also a key factor that influences future attendance. On the other hand, results highlight that different consumer segments may benefit from ad hoc policy strategies. Although, the empirical investigation is based on a specific museum, the paper offers an overall theoretical framework that can be generalised to other cultural sites.