Context: The city metaphor is widely used in software visualization to represent complex systems as buildings and structures, providing an intuitive way for developers to understand software components. Various software visualization tools have utilized this approach. Objective: Identify the influence of the city metaphor on software visualization research, determine its state-of-the-art status, and identify derived tools and their main characteristics. Method: Conduct a systematic mapping study of 406 publications that reference the first paper on the use of the city metaphor in software visualization and/or the main paper of the CodeCity tool. Analyze the 168 publications from which valuable information could be extracted, and build a complete categoric analysis. Results: The field has grown considerably, with an increasing number of publications since 2001, and a changing research community with evolving interconnections between groups. Researchers have developed more tools that support the city metaphor, but less than 50% of the tools were referenced in their papers. Moreover, 85% of the tools did not use extended reality environments, indicating an opportunity for further exploration. Conclusion: The study demonstrates the active and continually growing presence of the city metaphor in research and its impact on software visualization and its derivatives.