"I think of New York as a puree and the rest of the United States as vegetable soup"

The speaker is most likely sharing their point of view that New York is the focused significance or essential part of the United States, like a puree which contains only the most delicious and important aspects of veggies. In contrast, the remainder of the United States is seen as a mix of numerous components, like a vegetable soup that is less pure and more weakened.