"It is distinctly possible to remain too long at the Fair." - The fair is usually a gathering of people for the commerce or entertainment. It is a place where everything is fun, new, and within reach. However, it is only located in a limited space and once you have explored all that there is to explore, all the things you've enjoyed in your first perusal would gradually lose its charm until you get fed up with the fair. That is what she meant by that.
She stayed too long in New York because she said so. Her initial plan was to stay for only six months, in the end, she stayed for eight years.