Well, I live in New Orleans, where it would be easier to list prominent artists who have NOT played.

I can't even think of a good answer to that modified question ~ that is, I can't think of any prominent musician who has NEVER been here. I can think of a couple of prominent rock-era acts who avoided/missed New Orleans for years but eventually did play here:

Grateful Dead: Their first (and for many years, their only) visit to town was to open the city's first "underground" (hippy-style) dance-concert venue, the Warehouse (more preccisely, "a" warehouse ~ the posters always read "At A Warehouse, [address] Tchoupitoulas St.") This was shortly before I first arrived here, probably 1966-67. Band members were arrested for possession of marijuana (what a surprise!) and, although their record company eventually got them off the hook, they didn't come back for a couple of decades. You might recall that the incident is memorialized in a GD song lyric, "...busted / down on Bourbon Street..." (My future brother-in-law Charley, incidentally, had his picture in the paper the next morning handcuffed to Dead member Rod "Pigpen" McKernan.)

After many years, New Orleans downtown Seanger Theater finally became a semi-regular tour stop for the Dead, so in the 3end they relented in their determination never to comeback again..

Eric Burden: He made his first (and perhaps only) appearance in New Orleans (setting for the lyric to his best-known recording, "House of the Rising Sun") one late-1980s weeknight at Tipitina's, to a less-than-full house. I'm unsure of the date, but I do remember that the Animals had long since broken up; I happened to be there and can report that Eric was looking pretty old. Guess what he did as an encore? (Very nicely, too...)