There are several synonyms for the phrase "Austin-to-Baton Rouge direction." This phrase refers to the geographic area or direction between two cities - Austin, Texas, and Baton Rouge, Louisiana. Some synonyms for this phrase include "southwestern direction," "Gulf Coast direction," or simply "Texas-to-Louisiana direction." Each of these phrases can be used to describe the same general location or direction. These synonyms are useful when giving directions or describing a general area, particularly when traveling or navigating through the southern United States. It's always handy to have a few synonyms in your vocabulary when exploring new areas!