I would like to ask for your help to describe a coffee shop that is very cozy for chatting.
You can try intimate.
Intimate- characterized by or suggesting an atmosphere conducive to privacy or intimacy; warmly cozy
The little coffee shop had a very intimate atmosphere, making it easy to conduct deep, personal conversations for hours on end.
You could also use comfy.
The comfy coffee shop was a great place to have private conversations.
If this is for some formal school project or an essay, I would go with
snug and avoid
comfy as it is informal. Otherwise, it is all good.
Homey, homely, snug, or commodious are words that can be used, in addition to comfy and intimate.