An easier way than explained below is to use a Google Drawing in Google Drive.

This is an example of an image map. Click on the words to go to the appropriate site.

Below example, the code has been converted to a gadget.

Shiawassee Arts Center Shiawassee Regional Chamber
To make an image map work you have to edit the HTML. I used an Image Map program to create the code. 
The program I used is MapEdit
Here is the HTML of the result:
Note: Hosting these files in Google Drive is being discontinued so I recommend using DropBox instead. You can also host your XML files in a file cabinet page in a Google site.  HTML files will have to be converted to gadgets.  See THIS SITE
<DIV style="DISPLAY: block; TEXT-ALIGN: left"><IMG src="" useMap=#imagemap border=1></DIV>
<DIV><MAP name=imagemap>
<AREA title="Shiawassee Arts Center" shape=RECT alt="Shiawassee Arts Center" coords=24,5,195,39 href="">
<AREA title="Shiawassee Regional Chamber" shape=RECT alt="Shiawassee Regional Chamber" coords=76,49,392,87 href="">
<AREA shape=RECT alt="" coords=0,0,0,0></MAP></DIV>

Creating an image-map (from "prac")

More info  

Gadget code:

<?xml version="1.0" encoding="UTF-8" ?>  
  <ModulePrefs title="imagemap" />  
  <Content type="html"> 
<div style="display:block;text-align:left"><img border="1" src="" usemap="#imagemap"></div>
<div><map name="imagemap">
<area target="_blank" alt="Shiawassee Arts Center" coords="24,5,195,39" href="" shape="RECT" title="Shiawassee Arts Center">
<area target="_blank" alt="Shiawassee Regional Chamber" coords="76,49,392,87" href="" shape="RECT" title="Shiawassee Regional Chamber">
<area target="_blank" alt="" coords="0,0,0,0" href="" shape="RECT"></map></div>     ]]>