On February 1st, I hit a sink hole on a main road in a SC city. There was $500+ damage to my car. I live in NC so we got the car repaired and filed a claim with the city. The lady representing the city called me today to say that since the sinkhole was unknown to them, they are not accountable for damage. She cited the (Tort Act?) which I didn't understand.

I have spoken with several lawyers and they basically are saying that with such a small amount of damage, I would be crazy to want their legal services. They say I'll spend more money paying for their time than I stand to get from the city.

Am I going to have to eat the repair bill or can the city be help accountable?

I am not a lawyer but based on my experience as a Highway Engineer, my understanding is that you need to prove negligence--that the city knew about the hazard and took no action.
I think you should request a written evaluation of your claim at minimum.
You could request (via FOI Act) a copy of the Public Works Dept. complaint log (one may or may not exist) to verify that no calls were received prior to your mishap.
Unless you can prove that they did know about the hazard your options are few.

... She cited the (Tort Act?) which I didn't understand. ...

This law (probably a South Carolina statute) would provide that you have to comply with certain procedures to sue the state or, in this case, a city. Ask her for a citation and you can look it up.

If you comply with that, and it allows you to take the case to small claims court, what Smearcase said fairly maps out for you what you will have to prove and how.

Thanks for the responses smearcase and AK lawyer. This whole event has made me even more frustrated with insurance companies. If I file with my insurance it would be considered collision and my premium will jump. My deductible is 500 so I still would have to pay for the repairs. No win situation.

Did they at least fix the hole after your complaint? I hope so. Small consolation but maybe you saved someone else some grief. If you live in an area that has to plow snow especially, stay alert--there will be plenty more to come.