Didn't want you guys to think I'd forgotten to come back and thank you for all the great tips. It's just taken me this long to document everything to my blog, linked below.
To recap, though:
Day 1: Oysters and gumbo at Acme (awesome - I enjoyed the atmosphere as a first-timer, and dining alone), dinner at (blech) House of Blues. You can read about this travesty yourselves.
Day 2: Dinner at August (fabulous. Just wonderful. And I'm still dreaming about the desserts)
Day 3: Brunch at Delmonico's (again, amazing. Wonderful service, great food - for the most part). Dinner at Stella! (really enjoyed the meal, but service left something to be desired)
Day 4: More raw oysters & fried oyster po' boys than any 2 people should eat; lunch at the zoo (surprisingly tasty), ridiculously good jazz at Spotted Cat.
Thanks for ALL of your recommendations. I was so, so saddened to miss Brigtsen's, but we'll definitely make it there next time!