The 'Big 4' networks include ABC, CBS, NBC, and Fox. Many aspiring journalists see these stops and having 'made it' in their career, while other journalists would much rather work for themselves or other more independent news entities. Be honest about your aspirations without sounding like you want this opportunity only as a stepping stone.
"My greatest aspiration is to work for a publication where I can keep my integrity, and work on pieces for which I have a passion. It's also important to me that I am proud of the ethics that come along with my employer. If that happens to be a 'Big 4' down the road, that's great; however, it isn't my greatest aspiration as a journalist."
"My greatest aspiration as a journalist is to be known as a writer, reporter, and researcher with a unique angle, interesting stories, and integrity. I am more concerned about the types of stories I would be working on versus working for a Big 4. Also, for myself, that would likely require relocation which is not something I am entertaining at this point in my life."