New Orleans is not part of the City, for certain. New Orleans is (in Dredd's time) surrounded by Bayous, with the Burning Mississippi running past the city (and later, through and over, thanks to the Preacher).
New Orleans was a hell hole of crime with brothels, drug dens, slavery and much more besides that comprised the very worst of humanity. The place was destroyed a few years back by the 'Preacher' character (an ex-Texas City judge who found Grud (or possibly God, not absolutely certain which) who got very Biblical on the city's arse.
The Bayous have bred some really nasty bad guys and is a den of terrible and vicious mutants (although the Preacher also wiped out the worst of these as well).
Texas City judges did attempt to have influence there, but only in the most corrupt way and I feel quite a few of the more psychotic types in the force got to have fun bagging a few muties...
Texas City judges are not renowned for their honesty and corruption for them is a very serious problem (worse than in the Big Meg, perhaps even more than Brit Cit (who's Senior Judges consist of a right bunch of (insert rude word here).
I would go with Texas and Oklahoma. Areas outside the city would be under the juristiction of the City from time to time, but this would not be consistently enforced (maybe more than with the Big Megs Hot Dog runs, but not that much).
