Autocross is similar to a rally cross in which the events are held on paved surfaces ranging from airports to parking lots. An autoX is kind of like a mini road course. Similar to the rallyX, each organization has its own rules and guidlines in regards to the cars. Different setups put you in different classes, so be careful because a minor modification may put you in an advanced class in which you have no hope.
There are ton of courses around the Raleigh area and the autoX are held more frequently than the rallyX because of a higher turn out. THSCC has a calender of events. There are a lot of organizations around NC that hold autoX events, so it boils down to which one is closer (unless you do not like a specific organization).