So it seems that I'm learning quite a lot already as I have to go back and correct something that I mentioned in my second post. I basically assumed that the musical roots of jazz were African. This is way too simplistic a thing to say. Sure, the slave trade from Africa brought along a lot of spirituals that made their way via the Caribbean to the American south. But we also have to consider how even that music got mixed up with the Spanish flavour of music in that neck of the woods. This mix of African and European (in particular French) influences is at the crux of the debate regarding the "origins" of jazz.
Which brings up the next issue - why New Orleans specifically? Geographically it seems obvious enough with its proximity to the Caribbean and the rhythms it soaked up from there. There was also the influence of the creole population - people of mixed race descended from African and French settlers predominantely in this region. Up until the end of the 19th century I think it would be fair to class them as having property, power and a high level of education. This all changed however with a Supreme Court ruling in 1896 (Plessy v Ferguson) that basically upheld the Jim Crow laws of the time and effectively allowed for racial segregation. This forced the creole population into a situation where they could not integrate socially with the "white" population. Musically, this provided the essential mix of high musicianship provided by the creoles of color with the more guttural form of blues found in New Orleans at the time.
New Orleans was also pretty much party central at the turn of the century (and probably still is). Being a vibrant port linking the two American continents and the Caribbean link to Europe it isn't hard to imagine the scene of parties, cribs and brothels with the particular music being generated that was specific to New Orleans at the time. This also included piano music - some places were probably too small to accommodate the larger "jass" bands so the piano took a foothold as an important instrument in the development of jazz.