Hmmm... 10-4, that's a tight time span
OK- A good place to start is at Cafe du Monde. Fun place to get your bearings. (unless there is a line for the tables, then skip & go later). You'll find all sorts of little shops on Decatur street that will be fun for shopping. The French Market is a fun shopping spot too. The expensive stuff is in anything that looks like an art gallery or antique shop, usually up on Royal St.
Margaritaville will often have a musician playing, but usually at nights or happy hour, so I am unsure about Sunday afternoon. Check their schedules now for similar days of the week.
Consider a Jazz Brunch somewhere for Sunday morning Jazz. Reservations a must if you do this. Check around restaurants to see if they offer this, and plan accordingly- Maybe Gumbo shop has one? I don't get a warm fuzzy there, so it's never on my 'must do' list in New Orleans.
Sunday Brunch is big there, if you do plan for a brunch, get there early, or make a reservation in advance for the best times/locations (like now...
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Looking for any culture? I can comment on some non-drinking semi-educational/cultural activities if you want. Check out these FQ places online: Ursuline Convent, Hermann-Grima House, Beauregard-Keyes House, Cabildo, Presbytere. If those types of things are of any interest to you, let me know and I will be happy to share opinions on those.
We are used to finding live music pretty much everywhere at every hour in New Orleans, but if you are looking for something specific, it can be a bit more of a puzzle. Bars are quite smoky there, but may be OK enough for you in the daytime.
Here's a starter site for Music listings:
http://www.nola.com/music/
Bargain Picturesque trip: if you can time it right, take the free ferry to Algeirs Point. Stay on & ride right back across the River. Nothing to see in AP with your short time span. But you can get some great views of Jackson Square from the River and if the Steamboat Natchez happens to go by, it looks fabulous in photos
Always look up for wrought iron balconies, and at doorways- they are really great in the FQ.
ALWAYS stay with recommendations from friends and guide books you trust for food in NOLA. Don't waste your time there on somewhere with a waiter standing outside handing out menus. Just don't do it. You will have average food at best, and there is no reason to settle for average here, where there are so many outstanding choices.
Have been to NOLA w/ a pregnant friend- just be careful of the heat, she got tired FAST when it was hot, but of course that will vary. Don't forget a hat. The sun can beat down, even in the dense FQ.