Addressing issues of social diversity, we introduce a model of housing transactions between agents who are heterogeneous in their willingness to pay. A key assumption is that agents' preferences for a location depend on both an intrinsic attractiveness and on the social characteristics of the neighborhood. The stationary space distribution of income is analytically and numerically characterized. The main results are that socio-spatial segregation occurs if -- and only if -- the social influence is strong enough, but even so, some social diversity is preserved at most locations. Comparison with data on the Paris housing market shows that the results reproduce general trends of price distribution and spatial income segregation.