In what location is county government primarily based in Georgia?

The county government in Georgia is primarily based in the county seat. The county seat serves as the administrative center for local government operations, housing essential offices like the courthouse, the board of commissioners, and various county departments. This location is specifically designated to facilitate the functions of county governance, allowing for efficient management and accessibility for residents who need to engage with their local government.

In contrast, the other options do not serve the same administrative purpose. City hall is associated with municipal government and pertains to cities, while the state capitol functions as the center for the state government. A community center is generally focused on recreational or social activities and does not operate as a governing body. Therefore, the county seat is the correct answer, as it embodies the central location for county governance in Georgia.