Is there a way that I can save my Playground books on my local machine/iPad files instead of using iCloud?

To *not* have your Playgrounds sync (on your iPad) you can go to Settings and your iCloud account at the top of the settings list. In there, if you tap on the iCloud option you should see a list of app using iCloud... you can toggle the switch for Playgrounds and you should be good to go.

On the Mac, go to System Preferences and tap on the Apple ID preference in the top row. In the list of apps using iCloud on this Mac you should see an iCloud Drive row with an Options... button. Click on the Options button, find Playgrounds in the list that pops up, and uncheck it. That *should* do what you want...