As long as your handgun is kept in a closed glove box or console, you can carry it loaded or unloaded pretty much wherever you go in SC. The exceptions to that are federal property (ie. military installations, etc), state or countyparking garagesor any school property. Your example of the parking lot of a restaurant that serves alcohol is a non-player.
The only time you must notify is if a LEO requests identification and you're carrying pursuant to a CWP. Carrying as you will be, in your vehicle only, you are not required to notify. That being said, if your gunis sitting on top of your registration when a cop pulls you over and wants to see your paperwork, it might be a good idea to mention it. My recommendation is to keep your papers and gun in different locations and say nothing. The less said the better.