I read this post before visiting New Orleans and took people's advice! I would restate/suggest again that the coffee at La Divina is the best coffee (they have stores on Magazine Street and in the French Quarter). The only issue is they don't open until 11am at either location, so if you need coffee in the morning you will have to try elsewhere. They also went out of their way on Magazine Street to locate a local bookstore for us, by one staff member calling his wife, very sweet and friendly.
For a earlier morning coffee, or if you want coffee and breakfast, I would suggest the espresso or latte at Stanley's in the French Quarter. While not as good as La Divina, it was pretty good and not bitter.
I also discovered that a group called SNOB - Society of New Orleans Barista's is working on improving coffee in New Orleans. See this cute blog story: http://nojuju.blogspot.com/2009/12/es...