A day just simply isn't enough
Your best bet with the time frame you have is to go directly to the Market
(park at the corner of Market & Meeting, 8 bucks all day)
and spend the day there. You can see the Harbor from there at Waterfront Park.
You can walk the Market area and see everyone's wares and there are fabulous places to eat.
I would recommend Hank's for seafood. Hyman's is not what it is hyped to be and isn't worth the money. My favorite restaurant downtown is High Cotton. Either place you will need a reservation.
You can also walk the battery, both high and low and see Rainbow Row. You will see many fabulous homes there as well. The *touristy* thing I would recommend is a carriage tour.
It is truly overwhelming if you have never been and that will be by far enough for one day. If you must go to the beach I would suggest Folly Beach but I don't know that you will have the time.
Oh, you will also want to drive across the Ravenel Bridge. Beautiful bridge!