Acacia's den is in that one deep forest tile on the east side, at least that's where I found it at a few updates ago. It's just a small cave with a campfire for light and a pile of leaves for Acacia to sleep on. It's not even a separate interior you have to load into like the dungeons. She'll sleep there all day then start roaming the deep forest tiles at night.
Oh? Interesting. I was sure that the devs would have hid it in one of the two backmost Deep Forest areas to make it as difficult as possible to reach. Although perhaps they are aware of just how frustratingly tedious the area is to traverse so they decided to throw at least a little bit of a bone our way. I will go there to explore myself for sure, thanks!