Some of the best events I have ever been a part of in Gaming have been April Fool's Day Events.
Here are some suggestions:
1) Zombie event. People log in and there is a new merchant in town selling suspicious treats. If you eat them you become a zombie. You can then infect other players by /bite (I would recommend this only work if you are within 2 yalms or some other close range). The effect of being a zombie is a green cast to the skin. You can still do all regular content. All effects end the next day.

Variations on this type of event would include everyone becoming a chocobo, or a lalafell.

2) Invasion event. One of the major cities is invaded by something. For example there could be aliens invading Ul'dah. Players can only defeat the aliens with "ray guns" that can be gotten from strange new merchants.

3) Random dungeon. The duty finder randomly drops parties in a new dungeon as a prank. The new dungeon is something short and fun like Turn 3.