It is, perhaps, a little passive-aggressive, and you could certainly make the argument that it would be better to just unfriend people you don't want to see on Foursquare, but if you don't know where they are, you won't be able to avoid them, either. But it's novel, and sort of utilitarian. And it will at least prevent awkward run-ins with someone you're trying to avoid!
One benefit of the location trend in social networking is that you can figure out where both your friends and enemies are at all times. Avoidr is a service that uses Foursquare to help you avoid people you don't want to see. Presumably these are people you've already become Foursquare friends with but now want to make sure you avoid. Avoidr is web-based, so you have to be near a computer to use it. Sign in using your Foursquare login, and designate "friends" you'd like to avoid. The site then gives you a list of places to avoid — places that your "frenemy" has checked into.