HDMI to VGA and HDMI to DVI do work.
Both VGA and DVI are both devices capable of supporting 1920x1080 (or higher) resolutions.
It's just digital vs analog at that point. And really, after working with both....Well...it's not that bad. (Though funny thing: There is an ad on the page for a VGA to HDMI converter xD Prophetic....)
Of course...something worth mentioning....Straight VGA will not carry audio....Nor will DVI...
So you might want to look into a box that has a VGA and audio inputs that can output to HDMI, or something like that.