The Garden District is a must see for anyone with the time visiting New Orleans. The best way to access this area is to take the 12 bus from the St. Charles Street and Common Street stop. The Washington Street cross street from St. Charles is the main street to access the Garden District.
I recommend doing a "free" walking tour. You can leave a tip afterward. They will take you along one of the streets and also through the Layfayette Cemetary No. 1. The tour shows a good amount of mansions and provides unique details regarding who lived in them from confederate generals to Sandra Bullock.
Just walking around the district is quite amazing. Be careful crossing streets and New Orleans drivers do not yield for pedestrians. Also there is a great coffee shop and book store to check out near Commanders Palace. I would highly recommend eating at Commanders Palace during lunch too.