Atlanta is 345 miles from the cruise port in Jacksonvile FL. That is a little less than a 5 hour drive.
The driving route from Atlanta to Jacksonville is very simple. Take I-75 south from Atlanta and then I-10 east to Jacksonville. The I-75/I-10 interchange is near Lake City, Florida.
This is a trip that is certainly doable in one day. Notable cities along the route include Macon (Georgia), Valdosta (Georgia), and Lake City (Florida).
It is wise to spend the night in the Jacksonville area the night before your cruise departure. Don't take a chance that travel delays make you miss your cruise. Here is information on hotels for cruise passengers in Jacksonville.
A cruise from Jacksonville FL is a good choice for Atlanta residents. The port is closer to the islands than more northern ports.