When you click the dropdown menu of "where" to save the file, you are just given something like "Favorites" and "Recent", but no option to navigate through your computer and choose a location. Is this intended or did I miss anything?
Click the down arrow [highlighted in red] for a full file-picker dialog.
Should be the same for any app, not just Chrome.
There's also another very neat trick, which Windows cannot do.
If you can see your destination folder open on your desktop, you can drag the icon at the top of its window, or any sub-folder within the window - & the file-picker will go to that location.
[Unfortunately not so easy to grab a picture of it in action, but I managed to fake it in photoshop.]
After you let go, Applications will change to Downloads.