According to the album, Paul's Boutique is in Brooklyn...but we all know this photo was taken in the Lower East Side. With a Paul's Boutique sign hanging up on the Lee's Sportswear storefront, the shot was taken at 99 Rivington Street, where Rivington and Ludlow intersect. Currently residing in this exact spot is a restaurant called Paul's Boutique, named in honor of the album.
This shot looking down Rivington Street from the intersection of Ludlow is also included in the album art (note the yellow street signs). On the left you can see the First Roumanian-American Congregation (89 Rivington Street) that collapsed earlier this year. Though it was 17 years ago, the area still has many a shop selling men's clothes, leather jackets and sportswear - with their product hanging out on the sidewalk, just like in this shot.
The Beastie Boys first started practicing together at 59 Chrystie Street (between Canal and Hester), just about nine blocks from "Paul's Boutique".