Max,
Teresa and I visited NOLA many years back (pre Katrina). We did quite a bit of leisurely riding and it was a great way to see the city.
As I remember we rented a couple hybrids that shifted poorly, but that didn't matter because there's no need for shifting. I don't remember the roads being too terrible.
I can't speak to what they are now.
Riding to the zoo, outlying cemeteries and music clubs in the university area was great. I was well entertained just looking at the local environment. Houses, trees, people are very otherworldly to a Baltimoron.

I don't remember where we rented from, but there must be a serious bike store near the univ.