I love Jazz, but I can't find any good jazz bands with a good vocalist these days. I can't exactly think of one with lyrics that would fit Baccano! either
But I'd have to recommend Michael Bublé's music.
And if you want actual jazz from the 20s/30s, I'd say George Gershwin and Louis Armstrong (probably the most well-known musicians in that time.)
As for non-jazz music, I've always wanted to see a Baccano! AMV done with Gorillaz. ^^'