Hey there, the best place to start with a quesiton such as this is: Go to the local permitting office that you want to do work in. Each project and GC is listed. You can probally find 100+ projects. Also, McGraw Hill, or Carolinas AGC, or the Charleston Business Journal are great resources.
It's best to have your portfolio and resume ready in a .pdf with a cover letter.
Sandy - there is a reasonable amount of new construction now in the Charleston area. There are also remodeling and landscaping companies who incorporate masonry work into their projects. You may want to try contacting temp agencies and searching the Yellow Pages for any category that might use masons to see if any of them are hiring and to check the classifieds on Monster and in the primary local paper The Post and Courier. There are also many job boards on-line in addition to these. Craigslist is another option, but we all know you have a lot of scams there. These are a few ideas that come to mind.