Since the latter part of 2020, SARS-CoV-2 evolution has been characterised by the emergence of viral variants associated with distinct biological characteristics. While the main research focus has centred on the ability of new variants to increase in frequency and impact the effective reproductive number of the virus, less attention has been placed on their relative ability to establish transmission chains and to spread through a geographic area. Here, we describe a phylogeographic approach to estimate and compare the introduction and dispersal dynamics of the main SARS-CoV-2 variants – Alpha, Iota, Delta, and Omicron – that circulated in the New York City area between 2020 and 2022. Notably, our results indicate that Delta had a lower ability to establish sustained transmission chains in the NYC area and that Omicron (BA.1) was the variant fastest to disseminate across the study area. The analytical approach presented here complements non-spatially-explicit analytical approaches that seek a better understanding of the epidemiological differences that exist among successive SARS-CoV-2 variants of concern.