The study of social networks --- where people are located, geographically, and how they might be connected to one another --- is a current hot topic of interest, because of its immediate relevance to important applications, from devising efficient immunization techniques for the arrest of epidemics, to the design of better transportation and city planning paradigms, to the understanding of how rumors and opinions spread and take shape over time. We develop a spatial social complex network (SSCN) model that captures not only essential connectivity features of real-life social networks, including a heavy-tailed degree distribution and high clustering, but also the spatial location of individuals, reproducing Zipf's law for the distribution of city populations as well as other observed hallmarks. We then simulate Milgram's Small-World experiment on our SSCN model, obtaining good qualitative agreement with the known results and shedding light on the role played by various network attributes and the strategies used by the players in the game. This demonstrates the potential of the SSCN model for the simulation and study of the many social processes mentioned above, where both connectivity and geography play a role in the dynamics.