Best free things to do in Charleston?

Walking on King Street is lovely, there are tons of shops to browse in, it is also located right within the College of Charleston campus which is gorgeous and historic. Everywhere you look you will find Historic Landmark signs and can read up on the history of many buildings! There is also the Gibbes Museum of Art - free

Folly Beach is a fun beach with tons of bars and restaurants. Check the city calendar for any festivals/events that might be going on. Though traffic and parking can be a pain. Other local beaches are Sullivan's Island and Isle of Palms.

You can easily spend a few days just walking around downtown - parking at the Battery is free and its a good starting point to walk toward Rainbow Row, down East Bay St, to Waterfront Park and turn off to the Charleston City Market. King Street is great for [window] shopping and on Second Sunday of every month part of the street is blocked off to traffic so pedestrians and their pets can walk down the middle of the street. Marion Square has a farmer's market on Saturday mornings. Wonder around South of Broad area to see some beautiful homes.

Walking, jogging, or biking over the Arthur Ravenel Jr Bridge at sunset or sunrise will give you a great view of the peninsula. 

Angel Oak Tree is a bit of a drive but pretty cool to see if you have some free time. There are several beautiful plantations/gardens, like Magnolia Plantation and Gardens, Middleton Place, Boone Hall Plantation, but those are not free (most of them are about $30 to enter).

Hope this helps you explore Charleston!