Where can you find a video game designer looking to buy original music for a new game?

Try looking in websites that either deal with video game music, or video game design. Ocremix.org is a great site for freelance musicians. Their work is not bought or sold, but I happen to know for a fact that people in the game industry keep their eyes on that site. Gamasutra.com is a great site for designers and people in the industry, but I'm not sure if purchases or deals take place there; I'm not familiar enough with the workings of the site.

Also keep in mind that a designer might not want to buy your music: would you rather buy a computer from some guy off the street, or from a place like CompUSA or BestBuy? Likewise, if you're unknown, even if you're good, there are still legal issues to iron out before anyone might buy anything from you, especially if your work is copyrighted (which it should be).

The ideal thing would be to actually get a job in a game company and get paid for your efforts.

Lastly, don't neglect the power of networking. Get to know some people in the industry, and spread word around that you're looking for someone wanting to buy your compositions. This might help you get your foot in the door, which is not easy, and nothing to sneeze at.