You can add an image map to a google site.
The code looks something like this (source):
<img src="workplace.jpg" alt="Workplace" usemap="#workmap">
<map name="workmap">
<area shape="rect" coords="34,44,270,350" alt="Computer" href="computer.htm">
<area shape="rect" coords="290,172,333,250" alt="Phone" href="phone.htm">
<area shape="circle" coords="337,300,44" alt="Coffee" href="coffee.htm">
</map>
There are online image map generators such as this one: https://www.image-map.net/
After getting the code, you can copy it from the image map generator site (a little tricky, but possible), and then add it as html to your google site. Obviously you need to have the image be publicly accessible.