My suggestion would be to lay very low in downtown Charleston. They passed a noise ordinance directly due to all the bikes coming down from Myrtle Beach during bike week and they strictly enforce it.
Murrells Inlet is a pretty ride. Park your bikes at Divine Fish House, have a beverage at Wahoos (cool outside bar that is waterfront but looks like an island) and take a stroll down the MarshWalk.
I would venture off McClelanville and head down to the waterfront. Very pretty area.
The Historic District of Georgetown is quite lovely and a picturesque little waterfront town. The River Room is waterfront and has been there for years and is very good.
Agree to eat at See Wee and to hit Poe's on Sullivan's Island.
Lastly, Shem Creek in Mt. Pleasant is lovely.
The SeeWee Restaurant is located on 17 between the two. It is a very casual place but fantastic food including seafood.
There are also great restaurants and bars in Mt. Pleasant before you go over the bridge into downtown Charleston. A quick look back over some of the recent Charleston posts will lead the way.
There's also a good bar on Sullivan's Island called Poe's Tavern that has good food and plenty of room to sit around outside.