You can look for a convertor of some kind, but you will need to be real careful. DVI to VGA was possible because DVI actually had a analog signal where the big "blade" part. So it wasn't a problem as long as the source supported DVI-A.
Now, aside from that there is the issue of HDCP, which is the REAL reason we have HDMI. The small cable and integrated audio was just a ruse to convince people to adopt it.
HDMI requires a handshake between the devices to prevent unauthorized playback. And stopping analog is EXACTLY the kind of thing they intended.
So make sure whatever device you look at, make sure it specifically spoofs HDCP.
And also make sure you are looking at HDMI -> VGA. There are lots of products that will convert analog VGA to digital HDMI.
But my slightly educated guess is that you will not find such a contraption.