To Baton Rouge: From Houston (per Google) is about 4:20. Arlington is about 6:30. Atlanta is a bit more than 8 hours; St. Louis is about 9:30. These are all one-day drives for a healthy guy in his 30s.
Or you can fly, although there's little benefit to flying if it's a 4-hour drive (between airport delays, connections, etc., it can take 4 hours even if the flight is 30 minutes in duration). The total flight times from most of these cities, factoring in the required time not in the air, is pretty similar - the actual flights will vary a bit in length (difference in air time from Houston vs. Atlanta is 30 minutes - 1:05 vs 1:35), but most of the total time is connections and airports, and that's pretty much the same for all of them.
St. Louis would be a longer flight, because there don't seem to be non-stops; and with layovers, it might still make more sense to drive (typical flight time from Expedia is 5 hours or more, with substantial layover between connections. Add ground time on either end, and you're pushing the driving time).
Pretty much a wash, actually - it's a travel day to get to Baton Rouge from any of these places.