Of course Pat O's is still here!
Check out the interior of St. Louis Cathedral, get a meal at any bar (the food is really good), drink on Marigny (Bourbon is really expensive).
Shopping wise, I like to browse around the Quarter area-they have some really neat shops hidden away. Take the streetcar ride and eat at Camillia Grill on St. Charles-food is really cheap! Kareoke at Black Cat is always fun, but the place is really crowded. Audobon Zoo and the aquarium are always fun for a day trip. So are the St. Louis Cemeteries (but only go with a tour guide because they can be really dangerous. #1 is where Marie Laveau is buried.) And even though it's really touristy, stop by the Riverwalk. There's a great pavillion in the food court with a nice view of the river.
And listen to street musicians, of course.
Are you keeping your visit limited to Garden District and the French Quarter?