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Neighborhoods are the building blocks of cities, and thus significantly impact urban planning from infrastructure deployment to service provisioning. However, existing definitions of neighborhoods are often ill suited for planning in both scale and pattern of aggregation. Here, we propose a generalized, scalable approach using topological data analysis to identify barrier-enclosed neighborhoods on multiple scales with implications for understanding social mixing within cities and the design of urban infrastructure. Our method requires no prior domain knowledge and uses only readily available building parcel information. Results from three American cities (Houston, New York, San Francisco) indicate that our method identifies neighborhoods consistent with historical approaches. Additionally, we uncover a consistent scale in all three cities at which physical isolation drives neighborhood emergence. However, our methods also reveal differences between these cities: Houston, although more disconnected on larger spatial scales than New York and San Francisco, is less disconnected at smaller scales.