I've heard two reasons for the choosing of the date by the perpetrators (if you believe it was the shadow government or terrorists). The first is that it was chosen for it's significance to the
Battle of Vienna that took place on September 11th 1863 which if had gone in the Muslims favor would have meant the conquest of Europe. I suppose the shadow government if they planned it would have wanted this as a scary reminder of the second time that invaders tried to destroy Western values and almost succeeded. A second Pearl Harbour. It can also be viewed in the terrorists favor, perhaps Bin Laden chose it precisely because he knew of it's significance as well.
But the problem I have with that is the fact that firstly, Bin Laden relied on Atta to decide the date on the attacks (according to the Nat Geo documentary I watched, 9/11, The War on America). He wanted it as soon as possible and feared the plot was discovered so was unlikely to be concerned with trying to live up to dates.
The second reason they may have chosen is for the simple fact that September 11th was a clear and cloudless day. As Ben Slimey put it, there was sun from Maine to Florida. I don't think that even Atta or Bin Laden would have risked chosing September 11th to commemorate the Battle of Vienna only to have it be a cloudy day where the pilot hijackers couldn't make out the skyline of New York and Washington while descending.
Just food for thought.