There are little adapters and adapter-cables, but those will not work on most monitors. They are a sort of "straight through" adapter which rely on the monitor understanding the signal a certain way. I bought a "HDV-G3000 PS2 to HDMI Video Audio Converter Adapter 1080P" which did not work.
Solution: Most people have RCA connectors, but what you really want is to have the highest-quality output from the PS2 and convert it using a device. So you take the high-quality cable for a PS2, which gives you S-Video output, and plug that into a converter box. The plus side is you can do upscaling and probably video switchboxing.
I ended up getting:
- INTEO BV20BK BNC to VGA Video Converter Adapter
- Round to Flat Power Plug Convertor - Black
An two-source audio mixer, so I can use one set of speakers for my computer and the PS2 is another project I only briefly looked at and haven't started yet.