The quarter south of Beaufain and Hasell Sts has the bulk of the antebellum mansions, shops, bars and cafes. At the southernmost tip of the peninsula are the antebellum mansions of the Battery. A loose path, the Gateway Walk, winds through several church grounds and graveyards between St John's Lutheran Church and St Philip's Church.
About half a dozen majestic historic homes are open to visitors. Discounted combination tickets may tempt you to see more, but one or two will be enough for most people. For the Revolutionary era, the Heyward-Washington House is best, and for antebellum Charleston, the Aiken-Rhett House wins in a landslide. Guided tours of the homes (some audio, some docent-led) run about every half-hour.
Aquarium Wharf surrounds pretty Liberty Sq and is a great place to stroll and watch the tugboats guiding ships into the fourth-largest container port in the USA. The wharf is home to the South Carolina Aquarium and is one of two embarkation points for tours to Fort Sumter; the other is at Patriot's Point.
Three significant plantations line the Ashley River about a 20-minute drive from downtown Charleston. All offer talks and tours concerning the role of slavery (though another, McLeod Plantation, located on the northern shores of James Island, is the best for an eye-opening and highly important experience on that topic).
Of the three on the Ashley River, Drayton Hall is the best for history buffs, as it features the oldest plantation house open to the public in America. Magnolia Plantation has great tours and wild gardens, with a Disney vibe. Middleton Place has the country's oldest, most elegant gardens and a fancy restaurant and hotel. You'll be hard-pressed to find the time to visit all three of these in one day, but you could squeeze in two (allow at least a couple of hours for each). Ashley River Rd is also known as SC 61, which can be reached from downtown Charleston via Hwy 17.
Also popular, Boone Hall Plantation in Mt Pleasant is where celebrities tend to get married, and is a very pretty spot for tourists and families. It's 11 miles from downtown Charleston on Hwy 17N.