Howsabout this.

Have each location have something like a 15% chance of being yours, not predetermined.

As you check locations, the chance goes up 2% or something.

Once you actually see a sleek, that is your location.

Some people will get lucky and hit their first loc, most people won't, and it is hard to abuse the system to get the loc you want, because you might well get one of the ones before it.