Yes, you would have to file 3 state tax returns.
You would report New York income on a non-resident New York state return. Which would include your New York only income.
https://www.nj.gov/treasury/taxation/njit23.shtml
Then New Jersey income on the New Jersey resident state return.
https://www.tax.ny.gov/pit/file/do_i_need_to_file.htm
South Carolina rental income on the non-resident South Carolina state return.
So you will clearly need to file taxes in your resident state of New Jersey, and since there is tax withholding you will also be filing a New York non-resident tax return. You will receive a credit for the taxes paid to New York on your New Jersey tax return.
That leaves South Carolina. The following all can be found here: Frequently asked questions
Do I need to file a South Carolina return?
If you are a nonresident or part-year resident, you are generally required to file a South Carolina return if you work in South Carolina or are receiving income from rental property, businesses, or other investments in South Carolina.
What are the filing requirements for a non-resident receiving income form South Carolina?
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.
And last this:
A nonresident individual who has South Carolina rental property as an investment in South Carolina should file the SC1040 and attach a Schedule NR Nonresident Schedule. Rents received from the rental of real estate, less all related expenses, are allocated to South Carolina providing the property is not used in or connected with the taxpayer's trade or business.
So I would say that you will be filing in all three states, assuming the LLC is a disregarded entity for federal tax purposes. If it is a Partnership, you may still have a filing requirement in South Carolina with the K-1 having source income.
Thank you for the question @SimonK
All the best,
Marc T.
TurboTax Live Tax Expert
27 Years of Experience Helping Clients