For whatever reason, the new Apple TV doesn't come with an HDMI cable and you'll need to buy it separately. Apple sells its own for $19, which is way more than what you need to spend on an HDMI cable.
Instead, check out Amazon, which offers perfectly good HDMI cables for less than $10. You don't need to pay a lot of money for an HDMI cable or any other type of cable for that matter. In fact, there's very little difference as far as quality is concerned between a cheap and expensive HDMI cable, so there's no problem with settling for the cheaper cable.