Depends on what county? What type of Charge? Take care of the case in NY now by hiring an attorney. They can schedule a surrender date. With my clients I schedule surrenders and negotiate bonds before my clients turn themselves in. GET AN ATTORNEY IN NY now. because if your picked up in any other place other then where the case is, you may have to wait a really long time in Jail. Then you will need 2 ATTORNEYS one still in NY and in the county you were picked up. Stop waiting and get an attorney.
Georgia will not extradite you to NY for a NY charge, the question is whether NY will ask GA to arrest you and hold you for NY to pick you up. If the DUI is a misdemeanor it is very unlikely. However, this problem will not resolve itself and generally will only get worse over time. At some point you will no longer be able to renew your driver's license. You may be arrested multiple times on the NY warrant in GA for failure to appear in NY, which will result in a temporary hold on you each time you have contact with the police until NY decides whether to extradite you. It can effect international travel and access to certain government programs if you have an active warrant. My advice is get a lawyer in NY and deal with the charge and get it behind you.