April 26th and 27th. Everything you need to know:
Show up early (like 6am). Pick up some coffee and a danish or bagel at a nearby coffee shop before you get on line. Then you're in business. Bring plenty of reading material (Cardinal background info is nice) plus a transistor radio so you can listen to draft gossip on WFAN or 1050.
The League typically will hand out mock draft contest forms for you to fill out. That will also make your wait go faster.
A bit of Draft Trivia - This will be the first time in recent memory that they didn't hold the Draft on Earth Day.