Spoiler warning: Plot and/or ending details follow.
While not a major holiday, Naomi Wildman and Neelix planned an elaborate celebration aboard the USS Voyager in 2377, including cheese pierogies, rock and roll music, and a reenactment of the historic first contact by Lieutenant Commander Tuvok. The day often meant a day off from school for Federation youth. (VOY episode: "Homestead", ST website: Startrek.com)
In 2381, Admiral Leonard James Akaar planned to have the USS Titan relaunched on First Contact Day, as part of a morale-boosting effort following the Borg Invasion earlier that year. (TNG novel: Losing the Peace)