Here’s a list of a great selection of New York furniture stores and their links:
BDDW, Blu Dot, Ligne Roset, CB2, Muji, Moss, Milan Luxury, Property, Conran, Kartell, White on White, Organic Modernism, Bobby Berk, Home, The Apartment, Room and Board, Crate and Barrel, Straight From the Crate, Urban Outfitters, Design Within Reach, Scandinavian Grace, ABC Home and Carpet, Vitra and i am not going mention IKEA!!