If you depend on the Notes App and don't have iCloud sync enabled you may find challenging to migrate notes from one machine to another or just backing it up.
As of today (2019-12) the following approach works (tested on High Sierra to Catalina):
# In the source machine
cd ~/Library/Group\ Containers/group.com.apple.notes
zip NoteStore-backup.zip NoteStore.sqlite*
cd ~/Library/Containers/com.apple.Notes/Data/Library/Notes/
zip NotesV7-backup.zip NotesV7*
Note: the V7 part seems to be associated with the version of Notes you are running so in the future this may change Note 2: Please bear in mind that this procedure overwrites the existing notes on the destination machine Note 3: This procedure backups the existing files, but you may want to have your own backup just in case Then you can copy the files two zip files into the target machine to the Downloads folaer and then run:
# In the target machine
cd ~/Library/Group\ Containers/group.com.apple.notes
mkdir backup
cp NoteStore.sqlite* backup/
read -n 1 -p "The following step will overwrite existing Notes. Press a key to continue: "
unzip NoteStore-backup.zip
cd ~/Library/Containers/com.apple.Notes/Data/Library/Notes/
mkdir backup
cp NotesV7* backup/
read -n 1 -p "The following step will overwrite existing Notes. Press a key to continue: "
unzip NotesV7-backup.zip