Where should I put .Appimages files?

You can put AppImages anywhere you want and run them from there -- even USB thumbdrives or network shares.

However, the official recommendation by the AppImage developers is to create an extra directory, ${HOME}/Applications/ (or ${HOME}/.local/bin/ or ${HOME}/bin/) and store all AppImages there.

Appimage files are applications which does not need any installation to use.

You just need to click on them to run/start the application and then close it when done. So, you can keep them in any directory you want.

I myself keep them in a directory called 'Apps' on the desktop so that they are handy when ever I quickly want to use them.

...or {some_mountpoint}/Applications