There's no single idea of "home" in Breakfast at Tiffany's, and this is what makes it such an interesting theme. For some, home is a feeling of belonging, and it doesn't matter where this is. For others, home has to do with the people who surround them and who make them feel safe. Home is not just the literal place where one lives. It's not the apartment or house that gives someone an address. It might be an entire city or the feeling of being near family, and it means different things to different people depending on their life experiences.
Home for these characters is the whole city of New York. It's the sights and sounds of this specific place that make them feel at home.
The idea of home is symbolic. For Holly, home is where the heart is.