Bike through the Garden District and admire the graciousness of the architecture, stop and stroll through Lafayette Cemetery , than mosey on over to Magazine Street for shopping and lunch. Better yet, head further uptown to Whole Foods, grab a sandwich and continue on to Audubon Park and picnic on the banks of the Mississippi. Relax, stretch your legs and hope that you are luckily enough to see a huge ship pass as she navigates down the river.
There are a organized bike tours that you might consider if you prefer a guide. They offer various neighborhood experiences and generally last 3 hours.
Remember, the more exercise you get while visiting New Orleans, the more you can eat!