Both were geographically downtown: Ornette's loft in Soho (Prince St.) and Slug's in the East Village ("Alphabet City").
Where the line is drawn is hazy. The Kyle Gann essay I linked to says "below 20th St.", but says that's arbitrary because The Kitchen is now on 19th.
I think the region might be expanded to Chelsea (which is itself vague, with northern boundary either 34th St. or "upper 20s"), because (for instance) the W. Eugene Smith loft was on 6th Ave. near 29th St.
"Downtown" refers to downtown Manhattan, below 20th Street (I'll pick that as an arbitrary boundary since the Kitchen, an important Downtown performance space, is now on 19th Street).