How can I make my Apple TV 4th generation show up as a device in iTunes on my Mac? I have an Apple TV 4th generation.

The iPads and iPods I am connecting show up in iTunes on my Mac. However, the Apple TV will not appear when I try to connect it using a cable.

How can I make the Apple TV show up in iTunes on my Mac, so that it's easier to push apps and media to it?
Unfortunately, you cannot push apps and media to your Apple TV (4th generation) using iTunes.

The only way to install Apps currently is via the tvOS App Store. I don't think you can use the internal storage on the Apple TV to store media in any way, it is just used to dynamically store data like apps and their downloaded or cached data.