The development of visual analytics (VA) systems has traditionally been a labor-intensive process, balancing design methodologies with complex software engineering practices. In domain-specific fields like urban VA, this challenge is amplified by heterogeneous data streams and a reliance on complex, multi-service architectures that hinder fast development, deployment, and reproducibility. Despite the richness of the urban VA literature, the field lacks a consolidated toolkit that encapsulates the core components of these systems, such as spatial data management, analytical processing, and visualization, into a unified, lightweight framework. In this paper, we introduce Autark, a serverless toolkit designed for the rapid prototyping of urban VA systems. Autark provides domain-aware abstractions through a self-contained architecture, enabling researchers to transition from design intention to deployed, shareable systems within hours. Furthermore, Autark's structured, tightly scoped interfaces make it well-suited for AI-assisted coding workflows, where LLMs produce more reliable code when composing from well-defined abstractions rather than generating complex solutions from scratch. Our contributions are: (1) the Autark toolkit, a serverless architecture for rapid prototyping of urban VA; (2) a comparative study of LLM coding effectiveness with and without Autark; and (3) a series of usage scenarios demonstrating its capability to streamline the creation of robust, shareable urban VA prototypes. Autark is available at https://autarkjs.org/.