Image Map Using Google Drawings
UPDATE: We now can insert the image map HTML code using the code option in the Embed menu. An advantage of the HTML code method is that when you hover over a link the cursor changes.
But I will leave the information below as an alternative method.
Note that Google sites does not allow code links to open in the same window.
I created a Google Drawing in Drive and made the text links.
I set the sharing to public and copied the link to it.
I used the embed URL function to insert it.
OR you can use the "From Drive" option and select the drawing.
Note that you can use text links or image links.
Another good tutorial
Google Drive, New, More, Google Drawing
Shapes, Select a shape
Insert shape on the image
Fill color transparent
Border color transparent