Saturday, 31 October 1987
The Ritz
New York, NY, USA
supporting Red Hot Chili Peppers, Royal Crescent Mob
[No setlist details]
New York Magazine @ Google Books
Flyer thanks to Lantz B.
"The Real Story" page 43
Daily News NY, 11 October 1987, page 9 City Light - 11pm, $14.50 advance, $15.50 on door

Note that RHCP site The Side has RHCP playing "Limelight" in New York that night:
RHCP Live Archive
On This Day:
Year Venue State/Country
1988 Kesha's Inn, Berkeley CA, USA
1990 Seattle Center Coliseum, Seattle WA, USA
1992 Globe Arena, Stockholm Sweden