I've found a good place to watch the Fireworks. It happens every 20:00-20:45 Ingame. I believe you can see Fireworks outside every city states. Here's the place with a great view of Fireworks(Where I saw it clearly):

Gridania-Next to The Wailing Barracks(Lancer Guild) where you can see a huge space and trees.
Ul'dah-Ul'dah Monument[Upper] which is just next to the Ruby Road Exchange or Outside the Gate of Nald.
Limsa Lominsa-Just outside the Musketeer's Guild in the Bridge connecting to Another Room(Which then leads to Bismarck)