Urban air mobility (UAM) has recently emerged as a promising new transportation mode, with various potential use cases. Facility location problems are well studied and of significant importance for various transportation modes. This work introduces a vertiport location identification framework, focusing on demand coverage and infrastructure accessibility. An Agglomerative Hierarchical Clustering (AHC) model was utilized for the identification of candidate vertiport locations, along with a k-means algorithm, for comparison and validation purposes, based on an estimated UAM demand pattern. A genetic algorithm (GA) was then formulated, for the solution of the proposed Uncapacitated and Capacitated Vertiport Location Problems (UVLP and CVLP, respectively), variations of the Uncapacitated and Capacitated Facility Location Problems. To evaluate and compare the introduced methodology, different existing facility location problems (FLPs) were considered and solved exactly using integer and linear programming. These are the Location Set Covering Problem (LSCP), the Maximal Coverage Location Problem (MCLP), and the p-median problem. The p-center problem was also considered and solved via a heuristic approach. The proposed framework is illustrated through applications in the Chicago Metropolitan Area, with the demand estimated on the basis of existing taxi and Transportation Network Company (TNC) data.