Green Hills is an affluent neighborhood in Nashville, Tennessee, United States. Green Hills is located south of downtown Nashville on Hillsboro Pike. Green Hills is within a region extending south to Forest Hills and Williamson County and east-west to Oak Hill and Belle Meade. The neighborhood is in close proximity to three area universities – Vander…Green Hills is an affluent neighborhood in Nashville, Tennessee, United States. Green Hills is located south of downtown Nashville on Hillsboro Pike. Green Hills is within a region extending south to Forest Hills and Williamson County and east-west to Oak Hill and Belle Meade. The neighborhood is in close proximity to three area universities – Vanderbilt, Belmont, and Lipscomb. The former streetcar suburb and urban neighborhood of Hillsboro Village is directly north across I-440.