Here's a sneaky way to do it using your web browser. Put the image on a page with the ismap attribute and an <a> tag around it, like the following:
<a href="nowhere"><img src="myimage.gif" ismap="ismap" /></a>
When you view that page with a web browser, move the mouse over the image. You will see the coordinates in the status bar along the bottom of the window. This works because the ismap attribute is intended for use with older server-side imagemaps, which had to relay the mouse coordinates back to a web server to determine what part of the map was clicked.