Sunday around Magazine
A lot of places have outside seating, so those are obviously stroller friendly. Some places I really like with outside tables are Stein's, Gott Gourmet, La Divina Gelateria and Sucre. If you're farther uptown, Slice has great pizza. Other than that, I will leave it to others who use strollers to give more specific advice.
La Divina Gelateria
3005 Magazine St, New Orleans, LA 70115