Day 1 for this when it comes to the US (whenever that is...)
And I like FFIV's story. It's not "deep", but it's a very grand adventure with a nice sense of scale. The way your world expands - you start out on a small continent, then expand to the entire overworld, then discover there's a huge underworld to explore, and finally ride a giant whale to the moon? - is just great and very satisfying.
And the characters are still pretty memorable, even to this day. They don't have the deep characterization of later FF games, but they were colorful, and most of all distinct - as much as I appreciate character customization in the later games, I think it can steal away from giving characters unique identities in both gameplay and plot. If anyone can cast Ultima, or wield the most powerful sword for 9999 damage, you lose a sense of how each character has a role to play within the party and in the story, and how the characters support and interact with one another.
With FFIV, the fact that you couldn't change jobs meant that you learned to deal with each characters' strengths and weaknesses (e.g. you always had to protect useless Edward) and grew attached to the individuality of each character. Edge will always be kickass for throwing daggers, Rydia is great for casting Bahamut and Meteo, etc. I did like that they included some party customization in the GBA port, though.
And while FFVI's music was better overall, FFIV's music was still pretty great (especially the bridge theme before the last battle, which was just epic, and the Zeromus theme - those trumpets/horns get me every time).