Notes won't sync via IMAP in macOS Sierra
Solution 1:
I was quite desperate with this issue as well after a clean install of High Sierra, here is how you setup Notes.app to find the correct imap folder:
System Preferences > Internet Accounts > [your account] > Advanced...
Check if your Path Prefix is set correct. In my case this was blank which worked fine for Mail.app but had to be set to INBOX to work for Notes.app
I hope this helps somebody.