At long last, the new New York Public Library branch in Soho is ready. The Mulberry Branch will have its grand opening, on Mon., May 21, at 3 p.m., at 10 Jersey St. (between Mulberry and Lafayette Sts.). A natural for Soho, the branch will have a focus on the visual arts and feature works on display by local artists. Also, in recognition of Little Italy there will be a special Italian section.