Saturday the 17th sounds pretty good based on using the approximate below timezone... as that makes it Sunday morning for us.
Doing a quick play around at
http://www.worldtimeserver.com converting times around, it seems that if you set it around 3pm New York time, it works out ok for the US East Coast (daytime), United Kingdom (early evening) and East coast of Australia (early morning), which are the key areas for usage statistics.
Obviously you could convert that into any specific timezone... but that works out for the maximum userbase of this forum. If you did it on a Saturday, that keeps the East and West coasts of USA, and United Kingdom, all on the same day. It puts Australia onto the morning of the following day, being a Sunday. Perth would be early morning, though there is not much userbase here from Perth to warrant stuffing the majority of the userbase around.
You could even have a second time, ie. 3 or 6hrs later, which would put most of USA into early evening and would allow some other places that would be dark in the morning, to participate at early morning times instead (daylight). This gives people two options, even attend both if they desire.