I've got a few buds who are bartenders in the Quarter, they mostly live in the Bywater/Marigny areas, and in Esplanade Ridge. About half of them don't own a car and bike it to work because they are close enough.
If you are looking for something more inbetween, Chalmette/Arabi or New Orleans East would put you near enough to I-10 for a commute to Slidell while keeping you in/near the city, however you would have to rely on a car/motorcycle.
The other option is to stay in Slidell near the lake, (personally, I would be a bit gun shy about living near the lake), which would put you closer to the school, but quite a bit away from the Quarter.
I would think that the cheapest rent option would be in Chalmette/Arabi and the East, but I haven't looked into rent prices so don't quote me on it

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All of this is assuming that you choose to bartend in the Quarter and not in Slidell.