Public transportation with high ridership rates is not only a sustainable alternative to automobile travel but also a crucial transportation mode to support zero-vehicle households, vulnerable populations, and marginalized communities. The reliability of the public transportation system is important in encouraging choice users to take transit. Extreme weather is one of the most common factors affecting the operation of public transportation. While departments of transportation and municipal governments are becoming increasingly aware of public transportation system vulnerability to extreme weather conditions, it is difficult to prioritize transit investment in reliability without a clear understanding of the costs. This study presents a framework to assess transit network robustness to extreme weather events at the city level, using open-source data. The analysis first constructs transit networks using open-source GTFS data, followed by a robustness assessment with scenarios informed by FEMA flood information. Network analysis is then conducted to assess the overall characteristics of the system. A large-scale analysis of 19 of the most populated cities in the United States identifies network features relevant to the transit network's robustness. Our analysis shows that 100-year and 500-year floods significantly influence the transit network, cutting off peripheral transit stations and causing the entire transit network to shrink. The evaluation and benchmarking approach proposed in this study is proven useful in assessing the flood risks of the transit network. Based on the analysis, most transit networks studied do not have the capacity to withstand 100-year floods.