I agree with the need to consider the placing of a cache carefully. In some ways that is why I queried averaging, because someone looking for a cache is not going to get within a metre or so. Averaging may give one a false sense of accuracy.
Obviously to get a good signal is important. But then also to remember that when a person homes in on the cache there is a good change they will only be within 5-10m. So the place of the cache should be good enough to allow them to do a systematic search within a 10 metre radius and find it. A hint may help here.
The etrex gives a location accuracy on the satellite page. Is this a DOP? When placing a cache people should look at the accuracy given by the GPS device and then consider whether someone that distance away in any direction could find it.