Save images locally ONLY - Never to the Cloud?

As the other have said, it saves directly onto the local drive.  Now as Adobe branches out to having mobile apps with more parity with desktop apps,  I can see them having the ability to save into the cloud as the primary option,  in order to seamlessly work on documents between your desktop and mobile device.  But that's just me speculating

Despite the rather misleading Creative Cloud name, the application behaves just like it always has. It installs and runs on your machine, and saves to physical drives on your machine. There's no cloud storage unless you specifically want it and go look for it.

The only "cloud" aspect is a new licensing model where your account is charged monthly, and the app calls home to verify once a month. It will continue to work for up to 99 days even without an internet connection.

Typical Photoshop work results in file sizes that aren't really practical for cloud storage anyway. Yes, I know internet bandwidth keeps improving, but so does average file sizes. I'm not sure the two will ever catch up.

Yes, that is the default behavior.