So many good ones here in Houston, it really boggles the mind. But if I had to settle on one, overall it would have to be Mark's. http://www.marks1658.com/
For a steak, can't beat Ruth's Chris: http://www.ruthschris.com/Steak-House/3828/Lafayette Seafood, its Cafe Vermillionville, atmosphere is subperb with a good wine list: http://www.foodtrekker.com/destinations/usa/louisiana/cajun_country/?ref=0000001984
It's kind of hard for me to pick a best in New Orleans, so I'll put what my favorite is when I go back to my home town in Morgan City\BayouVista http://www.tampicos.com/locations.html It's actually the only decent place available so it's an easy choice. Actually pretty surprised they have a website. They serve their Salsa hot, which I love. Don't really understand the cold salsa.
Galatoire's in the Quarter is always one of my favorites. I just want to order a little of everything from the menu every time I go. Others: Brennan's Antoine's Windsor Court Grill Room