American Airlines has round-trip flights from Dallas (DFW) to New Orleans or Chicago (MSY, ORD) for $138- $158, NONSTOP. Flights December to May. Extended weekends available. Origin/Destination reversible. Dates over Christmas are available for New Orleans.
A Carry-on bag and also a personal item is allowed for free on American. You can avoid paying for seat selection by accepting the randomly assigned seat at the gate.