The only train that will allow you to make a round-trip in one day is the Crescent. The quickest turn around time would be to Meridian, Ms. It's about a four hour trip, and the turnaround time is about three hours. You would leave around 7am and be back for 720pm. Only other option would be for you to take the train up and maybe take the Greyhound bus back.
Amtrak offers train travel north, west, and east out of New Orleans. The problem will be returning by train the same day. Check with Amtrak online, or at the rail station.
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