Several of the historic churches will allow non-members to use the church but require additional fees or that you are a member of that particular faith/ denomination. Call around. Most churches have secretaries that are available during the week.
First Baptist Charleston
First Baptist Church, French Huguenot, Unitarian Church, Circular Church, Redeemer Presbyterian, St. Luke (i think). Some of the other religions, Catholic, Luthern, etc., will allow you to get married there as long as one of you is a member of a church of that religion.
When I was looking here were the ones I found but I would check the website to verify as it was a little bit ago:
First Baptist, 2nd Presbyterian, Bethel UMC, Trinity UMC, First Scots Presbyterian, French Huguenot, John Wesley UMC (West Ashley), Circular Church.
Click on each tool to see a sample.