It depends on what you want to do. To actually become a professional astronomer for example it is almost essential you go to a top school because competition is so brutal. This is what MathAmateur was saying. For engineering, there is more work to go around but it is still competitive. Places like Google, Intel, and Apple do most of their recruiting at top schools, but if you aren't shooting for a high-level super high-pressure career a smaller school is fine.
As to your question, it really depends on the field. Most of the big state colleges are OK in engineering. In Louisiana, Tulane is well regarded, Louisiana Tech less so but it isn't a bad school. Plenty of people get jobs who go there.
One thing to keep in mind is that the smaller, less well-known schools are mostly known regionally. If you go to Louisiana Tech you'll have a much easier time finding a job in the southeast than if you go to East Washington State University, for example. My point is if you really want to live in a specific region, go to school in that region or go to a top-name school.
If you want to stay in the Southeast, the best school, hands down, in Georgia Tech. It is almost on par with the big names like MIT and UC Berkeley. Also really well-regarded in the South are NC State, University of Tennessee, and University of Florida. Texas has a lot of great schools including UT (Austin, Arlington, & Dallas), TAMU, UH, and Rice. These are all what I would call "Second Tier" schools, meaning you won't be recruited for joining a startup as much as if you went to Stanford, Berkeley, Caltech or MIT but you can still get a great job.