Abstract: Human spatial behaviour, navigation and activity in cities are affected by visibility in the urban environment. In this paper we report on preliminary results for an ongoing research modelling pedestrians' search for urban activity as a possible realization of the random walk stochastic process. We represent the urban environment by means of a mathematical graph, which conceptualizes the relationship between urban activities and movement channels. The graph is based on visibility of possible navigational targets incorporated in the city street network. Random walkers, wandering on the graph, imitate aggregated visual search for the urban activities in the case study, the historical district of Tel Aviv-Yafo, Israel. The paper presents preliminary analysis of the agent-based simulation expositing a strong positive relation between the local and the global visibility properties of the built environment. Thereby, visual accessibility of the given urban layout is characterized and quantified.