Is there a way to download ESO files from another PC?

You basically won't save any bandwidth by downloading the client off another source. If there's no game installation so far, the game client will download just the most recent version of the game.

The whole launcher as well as the game client itself both are very portable. They do not rely on any registry settings. Only constraint is the fact that the directory structure must stay intact and there shouldn't be any other files in those folders (or next to them). (Only registry entries written are for the uninstallation process as well as the default client language.)

Steps you can do:

• Install the game to a location where you'd like it to stay. Make sure you install the client to a new or empty folder. Do not install the client to a generic path like C:\Games as this might cause the client to delete other non-game related files! Instead install to C:\Games\Zenimax Online or any similar location with no other files/folders.
• Cancel the launcher downloading the game client and close it.
• Move the whole folder (in this example C:\Games\Zenimax Online) to your portable drive.
• Connect the drive to your other PC and run it right off that drive.
• Once finished downloading and patching, close the game client and remove the portable drive.
• Back at home move the whole folder back into position.

The same process may be used later on for patching, since some patches might be quite big.

In case you know someone who's got the game installed and patched, you can of course simply copy the whole folder structure without first bringing your own files with you.