When traveling to Görlitz by car, you most probably will take the highway A4 coming from Dresden. Even when starting from Berlin you should consider passing Dresden using the highway, as this is the fastest way.
Parking areas within the city center are directly located on the Obermarkt or at the roofed parking deck CityCenter Frauentor, which is 5 minutes to walk.
See here the route from Dresden airport to our office in Görlitz, Obermarkt 17: