Shocked no one's mentioned the French Market in New Orleans. Excellent French Dip, chowder, and other area favorites. Great portion sizes. Non-alcoholic Mint Juleps and Beignets are available from a window next door.
Seconding Cozy Cone & Hungry Bear, as well. The new spot in Adventureland, Tropical Highway, also offers ample Dole Whip flavors (with much shorter lines than the window on the main thoroughfare) and some interesting-looking dumplings.