Greenville has a relatively new dog park and the downtown area is very dog friendly!
For some reason the dogpark website is not working but below tells a little about it and has some pictures.
http://www.pawspot.com/park-profile/...rner/park/963/ http://upstatelink.com/apps/pbcs.dll...9170802&Ref=PH
Downtown Greenville
http://www.fallspark.com/ http://www.greatergreenville.com/dev...nt/dtn_map.asp