The closest exit to Garyville is Exit 194 (Rte. 641)
Pasadena, Texas is halfway between Austin & Baton Rouge
Baton Rouge is pretty close to halfway...
The halfway point from Sparta, NC to Baton Rouge, LA, falls in or around Opelika, AL.
San Diego
Fort Payne, AL
The halfway point between Decatur, AL and Baton Rouge, LA, falls in or around Enterprise, MS.
Moultrie, Ohio is halfway between Charles Town & Jackson
Dallas comes very close.
Saguache, Colorado.
Ramah is closer to Baton Rouge but a close halfway point
The drive takes about 12-13 hours so the halfway point would be in the Tallahassee area.
The halfway point is Jane, Missouri.