This weekend is the biggest confluence of events related to Design week. Design stores across the city are unveiling new collections or exhibiting, and this weekend there is a Design Week - themed street fair on Gansevoort Street. The most complete directory I have seen listing all of the different events and exhibits is here: http://www.core77.com/nydesignweek/. I'm going to try to catch the Uncomfortable Conversations exhibit on Saturday.
This weekend also begins the International Contemporary Furniture Fair, a design fair primarily aimed at the industry but welcomes the public on May 18 (Tuesday). Tickets are a whopping $50 but, given that it is the last day of the fair, perhaps a sample or two can be had for a good price (bring cash). Buy tickets at http://www.icff.com.