I've spent tons of time in Greenville. The wholly-walkable downtown hosts lots of restaurants (recommended: The Lazy Goat), coffee shops, the Greenville Symphony Orchestra, and an extensive park along the river. Local breweries, nearby colleges - everything you'd expect from a small city renaissance, but Greenville's started 10 years early and is pretty well along now.
Sorry I didn't see this until now, but Travelers Rest is about 15 minutes from downtown. I would look into a house in the North Main or West End area if you want close to downtown. Send me an email if you need any more help!
