Charleston, SC. Downtown. Battery Park? I forget what it's called. Take the touristy carriage ride (historical informative) and walk through the old houses to peek into the gardens. Awesome!
SOTB...you won't miss anything if you don't stop.
You'll love the Smithsonian...whatever bits you want to see. The monuments/memorials are a must; Washington (you need reservations if they've opened it up yet), Lincoln, Thomas Jefferson,Vietnam War, Korean War, WWII. You get the picture.
Williamsburg/Jamestown are awesome.
Oh yeah, when you go across Lake Moultrie, look for "the hundred mile fish". It's a billboard with a fish on it that is 100 miles from the border. They have one going either direction. Okay, it's a stupid little landmark that's kindof a family joke.