A second hand LCD monitor with a DVI-D input will probably cost less than many HDMI-VGA interface cables, especially good ones (probably less than $50) but make sure it really has DVI-D, or DVI-I, not DVI-A as that won"t work.
you also need a HDMI to DVI-D cable, but these cost just a few dollar, as they contain just wires, no electronics.
Look at the monitors DVI connector, if it has two square groups of 3x3 pins, or a large block of 8x3 pins then it probably is a suitable DVI input connector.
If the connector contains not a single solid 3x3 block of input pins then its a DVI-A connector and no good.
If the documentation or specs of the monitor say it has DVD-I it is also okay, that is the older standard that supported both DVI-D and DVI-A.
One disadvantage is that a computer monitor normally doesn"t support audio (that is one reason HDMI was invented), so you need to use a set of amplified speaker boxes with a 3.5mm jack plug, as is common for sound card audio out.
P.S. you might want to share your experience with posters in this thread, which are talking about the same adapter you use:
for more info (with pictures) about DVI-D see: