The Chelsea Market is filled with great restaurants and speciality food stores and pop up shops. I love stopping in and getting a gourmet grilled cheese from Lucy's Whey or a healthy juice from raw food restaurant One Lucky Duck, while shopping for dinner ingredients at the Italian market Buon Italia. For a great sit down restaurant, I love The Green Table, which serves great farm to table food.
The New York Earth Room is an interior sculpture by the artist Walter de Maria that has been installed in a loft at 141 Wooster Street since 1977. Go see!
When I first visited NY in 2010 the New Museum left a permanent impression. I love the architecture and the concept of the piled-white-shoe-box look-a-like building at the edge of the Lower East Side neighborhood. The exhibition program is appealingly different, and the bookstore in the foyer is not to be missed!