Proliferation of shared urban mobility devices (SUMDs), particularly dockless e-scooters, has created opportunities for users with efficient, short trips, but raised management challenges for cities and regulators in terms of safety, infrastructure, and parking. There is a need in some high-demand areas for dedicated parking locations for dockless e-scooters and other devices. We propose the use of data generated by SUMD trips for establishing locations of parking facilities and assessing their required capacity and anticipated utilization. The problem objective is: find locations for a given number of parking facilities that maximize the number of trips that could reasonably be ended and parked at these facilities. Posed another way, what is the minimum number and best locations of parking facilities needed to cover a desired portion of trips at these facilities? In order to determine parking locations, areas of high-density trip destination points are found using unsupervised machine learning algorithms. The dwell time of each device is used to estimate the number of devices parked in a location over time and the necessary capacity of the parking facility. The methodology is tested on a dataset of approximately 100,000 e-scooter trips at Vanderbilt University in Nashville, Tennessee, USA. We find DBSCAN to be the most effective algorithm at determining high-performing parking locations. A selection of 19 parking locations, is enough to capture roughly 25 percent of all trips in the dataset. The vast majority of parking facilities found require a mean capacity of 6 scooters when sized for the 98th percentile observed demand.