Is there a good equivalent to OneNote for Mac that allows local save

Use Outline on mac and iOS (http://outline.ws/ ). Outline can edit OneNote files directly, no conversions needed, and it allows local saves The iOS version also works with just about every cloud service.

There are three OS X apps included with OS X. All free and found in your Applications folder.

1. TextEdit
2. Notes
3. Reminders

If you don't like any of them, then you can search with Google to find the many dozens of note taking software out there for the Mac.

Well, TextEdit handles all of those. You can browse for others at MacUpdate.

How To Safely Use Macupdate To Download Ad-Free Software

This site has both free and paid membership accounts. If you have neither then some software will be distributed as an installer wrapper that includes adware/malware you may not want. Such a download may appear on your computer like this: Firefox Installer.dmg. Delete the download and return to the main site where you will find a direct link to the developer's website. Use that link from which to download the software. Or a simpler way is to establish a free or paid membership to avoid problems getting adware with your download.

What features of OneNote do you use? If you're just using text this is easy, if you're using the whole range of stuff that OneNote can do, then you'll have issues with the Cross-Platform element.

Unfortunately TextEdit isn't cross platform, tho it is a good basic text editor.

I don't think you'll find what you're looking for with a cross platform element, unless the material is stored online.