We were in NOLA in September 2018. When will you be there? We plan on being there September 5-9 this year. We haven't decided where we are staying yet. Last year, we stayed in Marigny/Bywater and before that up river from the French Quarter...I think it was considered Downtown. I'm unsure of the neighborhood boundaries.
Pretty much anywhere in NOLA has great food. That said, we enjoyed the food at Latitude 29. Service can be slow when it gets busy but we had a great time hanging out at the bar right after it opened for the day. We liked the small plates at Manolito, a Cuban cocktail bar in the French Quarter. The catfish at Elizabeth's in Bywater was amazing! I recommend Bar Tonique on the edge of the French Quarter and Treme for the cocktails (they serve no food). We have been there four times and each time my wife got a gin fizz and every time the bartender (different each time) spent a lot of time making it properly. St. Roch's Market had a variety of vendors serving delicious food and cocktails. I think it was in Treme, just north of Marigny/Bywater. I could recommend more but, really, there is so much good food in NOLA.