According to
LeVar Burton, June 16 was officially Captain Picard Day. That works for me.
It's interesting he should say that since he was the one who was in the director's chair when "The Pegasus" was being filmed.
The episode "The Pegasus" first aired on January 10th 1994, if any day should be Captain Picard Day, it's January 10th.
Captain Picard Day is celebrated on June 16th because it is the equivalent date to Stardate 47457.1, mentioned in the Star Trek: The Next Generation episode entitled The Pegasus.
Except there's no canon reason to think that 47000.0 falls on January 1st at 00:01 and 47999.9 falls on December 31st at 23:59 and that days are rather evenly spaced between. In fact, based on First Contact Day on VOY, that is certainly not the case. Specifically, that April-5th holiday was celebrated on Stardate 54868.6.
It's interesting all this is being said, about Picard Day being on Jan 10 because that's when "The Pegasus" first aired.
I just went and Googled when the ENT finale aired and that episode actually aired on May 13, 2005. HOWEVER, the episode (which is based on "The Pegasus") was FILMED in during the month of Januaury, so yeah... January 10 sounds good to me.
Edit---
My mistake, "These are the Voyages" was actually being made in March. GAAHHHH!