I believe there are two 3v3 series played in this area. The Kick It 3v3 and the Challenge Sports 3v3. The Charleston Battery 3v3 tournaments are part of the Challenge sports series while the Kick It 3v3 is played in Rockhill.
Both of them hold their nationals at Disney. You can find more info on them from their respective websites.
http://www.3v3soccer.com/http://www.challengesports.com/There used to be a Myrtle Beach 3v3 (part of Challenge sports)but I think it has been stopped for some reason. (I may be wrong on that)