Not a native, but have visited many times. One of my favorite things to do down there is ride the street car. I think it is like $1.50 each way, or you can get something called a "jazzy pass" that allows you to ride all you want for a number of days. Riding down through the Garden District is amazing.
Also, New Orleans has to be one of the best wandering cities ever, especially if you have a high tolerance for drunks/beggars. There is so much random awesome music, street performance, and hilarious people-watching. I could walk around that city for hours. The Riverwalk down the Mississippi is always pleasant.