I was hoping someone could help me with this. I'm pretty sure I read somewhere that you can do HD on your monitor with the 360.. it was a very vague explanation, but mentioned you had to have your monitor on specific settings and resolutions or some such. Here's what I have:
21" Widescreen Samsung Monitor (max reso. 1680x1050 - composite, component, and DVI inputs)
360 w/component cable
My suggestion would be to just get a VGA cable for the 360, otherwise get a VGA to Component adapter... the former will probably be easier to find locally than the latter, though the adapter will likely be a little bit cheaper, but not by much.
Key thing as well will be that you will only be able to do 720p on your monitor, though it will likely look a little bit off, due to the native resolution of yours.