In recent years, taxis in multiple cities and metropolitan areas around the world have shifted to utilizing alternative fuel options. Such change has significant potential to reduce environmental externalities and can contribute to alleviating energy policy concerns. However, little work has been conducted to assess the tradeoffs between selecting various fuels for taxis, or to design alternative fuel taxi systems. These tradeoffs exist as a result of the differing costs associated with fleet replacement, infrastructure deployment, operations and maintenance decisions, and costs to users. This paper aims to address this issue by providing an optimization framework for the design of electric taxi systems, and an assessment of optimal costs associated with various options. We focus on comparing the costs of taxi systems made up of gasoline vehicles, hybrid-electric vehicles, plug-in hybrid electric vehicles with AC Level 2 infrastructure, electric vehicles with battery switching infrastructure, and electric vehicles with DC Level 2 fast charging infrastructure. This approach is based on transit systems design methods and focuses on developing an approximate analytic model for electric taxi systems, which can be expanded upon in future research, to address large-scale taxi systems design problems. Scenario results are presented for various city types.