All the big boys are here.....Bank of America, Wachovia, BB&T, Regions, etc....all with numerous branches and ATM's.
With that said, I would suggest Carolina First. They are based in Greenville, as is their parent company The South Financial Group. South Financial Group is the largest bank based in SC and in the top 50 banks in the US. Carolina First blankets the area with ATM's. They also sponsor many community events and use mobile ATM's at these events....Artisphere, US Pro Cycling Championship, etc, etc, as well as having an ATM inside West End Field (handy for beer at ballgames

).