eat some beignets at Cafe Du Monde, and some jambalaya and gator sausage somewhere (plenty of good options - I really liked the VooDoo BBQ and Grill).
The French Quarter has some interesting history but is pretty unspectacular unless you're there on a weekend or holiday. And even then, if you're a good God-fearing Mormon, it would be more watching other people have fun, rather than having any actual fun yourself.