I'm primarily building an App for use on Android devices with Cordova.
I have not been able to find anything in the Cordova documentation (or the WWW) about how secure it is to store data in the local storage as explained here:
Will other apps on the device have access to this data? How difficult is it obtain the data from the local store with other means other than the app working with it?
I'm asking this because if it is too easily available on the device then it would probably be best to encrypt anything that might be sensitive here?
localStorage is not a Cordova thing, it's a web thing.
No, other apps do not have access to another app's localStorage.
You could also add some encryption. Maybe check out MongOGX