Also not quite in the Quarter, but walking distance: Bon Ton Cafe, on Magazine St.--greaseless and crunchy, but not tempura style. Some of the best onion rings I've had. Be sure to get some crab au gratin to go along with those rings. :o)
While not in the 1/4, nor a "tempura" style, the mountain of O Rings rests on a paper towel.... and when you r table has polished them off.... take a look at the paper towel - nary a grease spot on it.