Savannah, Georgia:
Pros:
Centrally located
2nd largest city in the CSA (~28mil. population)
Inland port (and easily defendable from sea)
Cons:
Hot, humid summers
Prone to hurricanes (although better located than Charleston)
Prone to flooding
Atlanta, Georgia
Pros:
Centrally located
Railroad hub
Cons:
Small City (~3mil. population)
Hot, humid summers, chilly winters (but temperate compared to most cities of similar latitude)
Rainy
Mobile, Alabama
Pros:
Largest city in the CSA (~30mil. population)
Colorful culture and history
Large port (probably the largest in the CSA)
Cons:
Hot, humid summers
Wettest city in the CSA (and in the continental USA)
Prone to hurricanes
Proximal to Louisiana (but still somewhat centrally located, and easily defendable)
Montgomery, Alabama
Pros:
Centrally Located
Actual capital of the CSA IOTL
Central to cotton region
Cons:
Hot summers
Not coastal
Small city (~9mil. population)
Memphis, Tennessee
Pros:
Trade hub (Railroad & Shipping center of the CSA)
Slave capital of the CSA
Large City (~22mil. population)
Cons:
Hot, humid summers, cold winters
Rainy
Located on the border
Nashville, Tennessee
Pros:
Trade hub (and largest manufacturing capacity in post-Civil War South IOTL)
Somewhat large City (~17mil. population)
Mild humidity
Cons:
Proximal to US border
First major city to fall in the Civil War
Hot summers, cold winters
Rainy
Charleston, South Carolina
Pros:
Centrally located
Location of largest military school in CSA (The Citadel)
Consistent, mild climate all year
Colorful culture and history
Cons:
Not a city (~120,000 population even today)
Prone to hurricanes
Tallahassee, Florida
Pros:
Central to cotton region
Only state capital not captured in the Civil War
Consistent, mild weather throughout the year
Cons:
Not a city (barely 3mil. population by 1900)
Prone to hurricanes
Raleigh, North Carolina
Pros:
Built specifically as a capital
Proximal to a popular tavern (seriously, it was built because it was close to this tavern)
Cons:
Proximal to US border
Small city (~5mil. population)
Mild summers, but cold winters
... ... ...
Personally, I like Savannah, Charleston, or Mobile.