I guess this was inspired by my post in the other Avatar thread, so I guess I should post my thoughts here.
I had imagined it as a fourth season to the 'Avatar: The Last Airbender' series (Book of Air). The story would pick up right where the last season left off with the Fire Lord deposed and Zuko in his place. Zuko on the tip from his father sets off to find his mother.
In the mean time Aang and his friends are getting the change to finally enjoy a bit of peace. Though it's a bit bitter sweet for Aang as the last airbender. Teo (the earth Kingdom boy living at the Northern Air Temple) arrives with news for Aang, that they discovered evidence that there may be other Airbenders still alive. The rumors are vague but indicate the existence of a hidden nomadic Air tribe. With very little information to go on Aang sets out to find this tribe.
Azula who has also been deposed and has gone insane is held in prison with only her delusions to talk to. These delusions are of her former friends, brother, avatar and his friends mocking her of her loss. Her mother still trying to comfort her, but the visions of her grow more horrific and her father telling her how much of a disappointment she is at her failure. Which finally drives her to make an escape. Once escaped she is further driven by her hallucination to seek revenge on all those who she feels have wronged her.
There would be a filler episode where Sokka retrieves his weapons.
Aang would eventually finds the nomadic Air Tribe, but they have since lost the knowledge of how to bend. So Aang begins to instruct them in airbending.
In the end Azula loses all touch with reality and ends up destroying herself. Aang and the new Airbenders are seen training at a restored temple.
There is clearly more that could fit in this, but that is as much as I had thought of.