John Besh's Domenica is in the hotel. It is known for it's half-priced pizzas and drinks during happy hour.
Down the block is the well-regarded MiLa, highly touted by Bill Hunt and others on this board.
Other possibilities in the CBD are Besh's two other locations, Luke for bistro fare and August for fine dining (it's prix fixe lunch is considered a great value). There is also Bon Ton Cafe for cajun dishes like gumbo and etouffee.
Of course, your friend will also be right on the edge of the Quarter with Galatoire's, Mr. B's, and numerous other options nearby.