According to the Virginia Department of Motor Vehicles, VA will accept any valid learner’s permit subject to restrictions mandated by the issuing state as long as a person is at least 15 years of age and that person is accompanied by a licensed driver who is at least 21 years of age.
This is only basic information that the VA DMV gave us so we would advise that you contact them directly yourself to find out if South Carolina beginner's permit is accepted in their state for you to operate a car. If you are permitted to drive in Virginia then see if there are any other restrictions placed upon besides being required to have a supervising fully licensed driver who is at least 21 years of age.
As for your home state of South Carolina, the SC DMV told us that if a person holding a South Carolina beginner's permit or a provisional license, and wishes to use that credential to operate a motor vehicle in another state, they must contact that state's DMV office. Any person holding an out-of-state beginner's permit or provisional license may not operate a motor vehicle in the state of South Carolina.
So while SC does not allow those from out of state to use their beginner's permit or graduated license in South Carolina to drive, they do not stop those from SC with learner's permits from traveling out of state but leave it up to the state in which you are visiting to determine if your permit is accepted as a type of license or not.
When driving out of your home state with any type of graduated driver's license we would advise you to contact your home DMV as well as the Department of Motor Vehicles of any state in which you are planning to travel to (and want to drive in) to verify they accept your license type and to find out what restrictions they place on you if you do operate a vehicle there.