Unless I'm missing something (definitely possible), it would seem that the most direct method of connecting the monitor would be to use a DVI (M) to VGA (F) adapter plug the DVI side into the Apple-supplied HDMI to DVI adapter, and then use the VGA side of the adapter to connect the monitor. I assume that the DVI side of the adapter is a standard DVI (F) female connector, which will accept a standard DVI (M) male connector. The Mac Mini comes with an 'HDMI to DVI adapter' (Apple's description), but I can't find any other information about that adapter on the Mac Mini description pages, nor can I find any photos of the adapter. I'm replacing the old iMac with a new Mac Mini, which has only Thunderbolt and HDMI connectors available.
I'm currently using it with an old iMac G4 (Gumdrop) via a mini-display to VGA adapter cable.
I have a perfectly good LCD monitor that has a VGA connector on its input cable.
