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For smaller towns in SC, Clemson is quite walkable (but it is a college town). Travelers Rest has a walkable downtown but will be missing some of what you are looking for like plays and concerts.
I'd also suggest visiting Chattanooga and Asheville for larger towns. Maybe consider driving through some of the smaller Western NC towns like Brevard to see if they would work.
This is a few years old now and looks like they haven't done another list of "top downtowns" since 2016 but Greenville was listed as the 3rd best downtown in the country by Moderator cut: link removed, competitor site. It's also been on quite a few other Top 10 listings. Might give you a little more info.