I like Irene's
Parkway beats Parasols hands down, especially since their kitchen basically moved to Tracey's down the street. As for burgers, skip Port of Call and head to Yo Mamma's in the Quarter. Peanut butter burger sounds gross, but it's worth it!
Katie's in Mid-City is extremely good (with some of the best chargrilled oysters), as is Elizabeth's in the Bywater for brunch. K-Paul's is about the only think worthwhile in the Quarter, as everything else is over-priced for tourists. Cochon is amazing, and Palace Cafe has a great New Orleans flair with reasonable prices for great Brennan-quality food.
If you want something off the beat path and like wine, check out Bacchanal in the Bywater. They have a great outdoor patio and recently added a very tasty menu.
Frankie and Johnny's also just reopened Uptown, and is a great, typical, old-style neighborhood seafood joint with delicious fried bell pepper rings.
Cafe Maspero - cheaper, fast and GOOD.
Camellia Grill - greasy spoon, almost always a line out the door though (go to the original on Carrollton though, NOT the bad one in the quarter).
Dante's Kitchen - GREAT brunch.
Tujague's - second oldest restaurant in NO, great experience and great food.
My kitchen, its uptown and the food is always good!