Network--based epidemic models that account for heterogeneous contact patterns are extensively used to predict and control the diffusion of infectious diseases. We use census and survey data to reconstruct a geo--referenced and age--stratified synthetic urban population connected by stable social relations. We consider two kinds of interactions, distinguishing daily (household) contacts from other frequent contacts. Moreover, we allow any couple of individuals to have rare fortuitous interactions. We simulate the epidemic diffusion on a synthetic urban network for a typical medium-size Italian city and characterize the outbreak speed, pervasiveness, and predictability in terms of the socio--demographic and geographic features of the host population. Introducing age--structured contact patterns results in faster and more pervasive outbreaks, while assuming that the interaction frequency decays with distance has only negligible effects. Preliminary evidence shows the existence of patterns of hierarchical spatial diffusion in urban areas, with two regimes for epidemic spread in low- and high-density regions.