Holden would consider it boredom, because he considers himself above all those mundane "phonies" at his school. He reminds me of students that I sometimes see at school, who are very gifted, but making poor grades, because they are not being "challenged" enough. Holden sees himself as 'above' the regular modes of education.
Freedom and boredom don't quite seem to capture the depth and complexity of Holden's situation. Maybe if we up the ante on boredom and start calling it ennui we begin to approach the philosophical urgency of Holden's state of mind.
If he craves freedom, I wonder what kind... I think we might say that he seeks escape - into innocence (an impossible escape) - and this escape bears some resemblance to an urge toward freedom. Yet "liberty" is not what he wants.
I agree with earlier comments suggesting that Holden is in many ways too shallow a character to have any really positive goal in mind, at least for much of the book. Instead he seems to some degree a drifter who allows chance and circumstances to direct his movements. Along the way, however, he encounters other characters -- such as the nuns -- who do seem to have definite, positive ideals and who have a positive influence on him.
I would have said that Holden was looking for an escape, rather than freedom. He doesn't expect freedom - this is too positive a concept for him. He seeks change, maybe the hope to re-invent aspects of himself and his life to be better.
He was about to be expelled anyway, and I think he really didn't know why he was going. He doesn't really know what he wants. When he gets there, he didn't even know who to call, which is why he wound up calling Faith. The incident with his roommate seems to have been a bridge too far, and it seems that New York City was a place to get away from the "phonies." Overall, I think it was perhaps boredom, perhaps freedom and adventure that drove him there, but he really seems to just want to get away.
Though there is likely some element of boredom that compels Holden to leave the staid and predictable world of the boarding school, it is also generally considered to be the case that he was looking for freedom or a way out of the horrible guilt and sadness he felt.
He is clearly looking for things in New York, he goes to see Sally and urges her to run away with him. He tries to sleep with a prostitute but wimps out at the last minute when he starts to understand that he just desperately wants someone to talk to.
He also wants to see his sister and to feel connected to something since he's been unable to do that since his brother Allie died.
I believe Holden had burned too many bridges to stay at Pencey, so it was an escape. He was easily irritated and was just beat up by his roommate. He mentioned leaving other schools without a 'goodbye' and how depressing it was. In his attempt to conjure up a goodbye he caused more problems. He admitted he only argued with Stradlater because he already knew he was out at Pencey.
Also, his family and friends were in New York. He decided to rent a hotel to have some alone time. I think being alone was truly an escape because of his personality. As a child he lost his brother, which was a big deal. Seeing people fall all over themselves for ridiculous materialistic-phony- things annoyed him. Holden believed he was "deeper" than most people.
Holden did seem bored or maybe ADHD, he always had to be calling someone or seeing someone, even though they annoyed him. He never just sat in his room and read. He constantly walked through the city and searched for people to talk to.