We spent a quick two nights in New Orleans and stayed at Hotel Mazarin which is right in the heart of the French Quarter. Walking to everything was perfect - tucked between Royal and Bourbon streets. Though it should have been really loud given the proximity to Bourbon street, the rooms face an inner courtyard which is pretty quiet. We were on the top floor so it may have even been a little noisier than other parts of the hotel.
They offer a really nice breakfast, berry infused water in the courtyard all day and very pleasant and courteous staff.
No complaints really - go enjoy!