At the beginning of the story, he gets a red hunting hat in NY. But why does he wear it indoors?

In the novel 'Catcher in the Rye' there could be several reasons why the main character Holden Caulfield chooses to war his hat indoors - it is up to us as readers to pick up the subltle markers and come to our own conclusions. We all arrive at a text with different experiences, so different readers will have different ideas speaking to them from a text. As a parent and teacher, for example, my observations would be that teens like to be different. The hat is a hunting hat - this is significant in terms of the theme of a 'catcher.' So, Holden is hoping to catch something. Also, teens (and particularly Holden) like to distance themselves from adult's values - so Holden is trying to advertise his 'uniqueness' and mark the fact that he is random and not 'phony.' He may derive a genuine sense of comfort from wearing the hat inside - perhaps it makes him feel close to someone or something it reminds him of. But he remembers to take it off at important times too.