As the operating system is 'web centric' there is no real need for any of your data to be stored locally.
However anything downloaded onto your device will be put into the default downloads location, which unsurprisingly is your local "Downloads" folder.
This is fine but it does however mean that such files are not automatically backed up and there is a small risk that they could be lost if, for example, you needed to re-install the operating system or perhaps you choose to experiment with the Canary or Beta development channels - for more details on this see the Beta & Dev Channels page.
To get around this low risk you can change the default location of your systems downloads folder to a safe location on the web. For example you could create a folder in your Google Drive [say #Downloads4Chrome] then go into local Settings and assign this as your system default.
From now on anything downloaded will actually be uploaded to #Downloads4Chrome in your Google Drive - neat.
If you have two or more devices they can each be configured to have their alternate Downloads folder as above. You can choose to share the same folder or assign different ones to each device.
Click here to read the handy article about "How to fix the 'cannot download file' issue in Google Drive on a Chromebook"