The State of TN has unveiled its Vaccine Informaton web site, which includes an interactive Vaccine Finder map (Mapbox/OpenStreetMap-based) of locations where one can receive COVID vaccinations. Both Health Department - sponsored locations and other Pharmaceutical \ Clinic locations are identified on the map.
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(Note: a Google-based interactive map is also available, but it has not been verified from KGIS whether that map is being maintained or not....the State website, as of 3/3/2021, no longer seems to be linked to this map. Therefore, any use of this map should be independently verified with the State of Tennessee).