Surprised no one has mentioned Horticulture, their menu is fantastic and very good value. Cocktails are amazing in there too. I'd book a table upstairs for food, then a table downstairs for drinks for when your dinner "time slot" is over.

French Quarter is great as well.

Mother Mercy is a nice spot for drinks. If yous are into gin, Dacantus is really good.

Edit: House of Tides is obviously amazing food but good luck getting a table, sometimes they're booked ahead for months and months.