Communities around the world have distinctive ways of representing language use across space and territory. The approach to and method of mapping languages that began with nineteenth-century European dialectology and colonial boundary making is one such way. Though practiced by relatively few linguists today, language mapping has developed considerably from its roots yet remains stymied by problems of ideology, representation, and data quality. In this paper, we argue that digital language mapping in hyperdiverse cities can both contribute to overcoming these problems and bring visibility and resources to communities using Indigenous, minority, and primarily oral languages. For these communities, official surveys like the census are often inadequate, leaving a gap that communities, linguists, and mapping experts working in partnership can address. Urban language mapping as a field should make space for Indigenous, minority, and primarily oral languages through geospatial visualization -- in terms that the communities themselves recognize and with a public policy agenda. As a case study, we present our ongoing efforts with LANGUAGEMAP.NYC to map the most linguistically diverse urban center in the world: New York City.