We present a model of the interaction of segregation and suburbanization in determining residential location. The model incorporates differential income between two classes of agents, a simplified market mechanism for the purchase of housing, and a simple geographic structure of one central city and four symmetrically arranged suburbs. Agents derive utility from neighborhood racial composition, the size of their lot, private amenities that are specific to neighborhoods, and public amenities that stretch across municipalities. We find that the public-amenities term leads to a positive-feedback loop in which migration to suburbs increases the public amenities in those municipalities while lowering amenities in the central city, thus sparking further migration. When the minority agents are uniformly less affluent than the majority agents, this dynamic produces discontinuity in segregation as measured by centralization. Such discontinuities are typical of first-order phase transitions. When minority and majority incomes overlap, significant regions appear over which there are multistable equilibria at high and low levels of segregation, along with considerable sensitivity to the initial distribution of minority agents. We discuss the implications of these findings.