Atlanta is 346 miles from the cruise port in Jacksonvile FL. That is 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 smart 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.