While cities around the world are looking for smart ways to use new advances in data collection, management, and analysis to address their problems, the complex nature of urban issues and the overwhelming amount of available data have posed significant challenges in translating these efforts into actionable insights. In the past few years, urban visual analytics tools have significantly helped tackle these challenges. When analyzing a feature of interest, an urban expert must transform, integrate, and visualize different thematic (e.g., sunlight access, demographic) and physical (e.g., buildings, street networks) data layers, oftentimes across multiple spatial and temporal scales. However, integrating and analyzing these layers require expertise in different fields, increasing development time and effort. This makes the entire visual data exploration and system implementation difficult for programmers and also sets a high entry barrier for urban experts outside of computer science. With this in mind, in this paper, we present the Urban Toolkit (UTK), a flexible and extensible visualization framework that enables the easy authoring of web-based visualizations through a new high-level grammar specifically built with common urban use cases in mind. In order to facilitate the integration and visualization of different urban data, we also propose the concept of knots to merge thematic and physical urban layers. We evaluate our approach through use cases and a series of interviews with experts and practitioners from different domains, including urban accessibility, urban planning, architecture, and climate science. UTK is available at urbantk.org.