Walt,
Not sure if Evergreen is a good place to overnight or not. The airport sits right next to I-65 and there is a Comfort Inn (phone 251-578-4701) about 5 miles up the interstate. Whether you stay the night or not, make sure you arrive before 5pm, I think their closed after that. Their phone number is 251-578-1274. Pensacola is a good overnight spot in terms of motels/resturants, but they'll charge you an overnight fee, seems like between $10-$15 or something like that. If you got time, maybe you could top off at Evergreen then head south to Pensacola. Or go DFW direct to Picayune MS, top off, then proceed to Mobile Regional or Pensacola regional for the night.