Free Tours by Foot offers tours pay-what-you-like walking tours of Charleston.  They offer two history tours and will be opening bike and food tours.  The company's main tour is the Historic Charleston Tour, a stroll through Charleston's historic downtown section.  Guides work effectively for tips, so you can fit this tour into any budget.  

Blackcat Tour offer a free Sunday Stroll at 11am.  Please check their website for updates. Avery Research Center for African American History and Culture - free public tours