I don't think the majority of apple users communicate their local files like notes through icloud.
You'd probably be wrong about that. I would suspect that most people just set up iCloud and let it sync all their notes between their Macs and iOS devices, which is by far the easiest way to use Notes.
Since for whatever reason you don't want to use iCloud, you can set up a Google or Exchange account, move your notes into that account in the Notes sidebar, and sync both machines to the same account.
If you don't want to do
that, you're probably just going to be manually going through each note and copying and pasting it out to .txt or maybe .rtf documents which you should be able to import using File → Import Notes. It does have an option to preserve folder structure, so conceivably you could make Finder folders full of your exported .txt or .rtf documents containing your notes, or just reorganize them after import.
If you want a notes app with more direct access to its files, I'd recommend Simplenote.