The fact that you have an LLC doesn't mean that your rental is treated any differently taxwise. Income is still reported on Schedule E and you have to file a return for the state it is located in, as well as your home state. NJ may have a credit for taxes paid to other states.
A nonresident individual receiving South Carolina income from wages, rental property, businesses, or other investments in South Carolina, must file an SC1040 South Carolina Individual Income Tax Return and Schedule NR Nonresident Schedule.
