I guess the Hotel Elegante is where the fancy folks stay.
Bryan's 797 on N. 5th Street is the Galatoire's of Beaumont. The food is very good in that high New Orleans style, and is priced similarly. (The address is 797 N. 5th St.)
Suga's is a good restaurant downtown that takes an haute cuisine approach to traditional southern favorites. They often have jazz in the evenings too. It's at 461 Bowie St.
For a cup of coffee or a quick light breakfast, you can't go wrong with Rao's at 2596 Calder or 4440 Dowlen.
P-Reaux's on MLK just south of Calder is a good centrally located cajun spot (eta: apparantly it's called the Seafood Shack now?)