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.