Zuko dies of old age. Has he many regrets and aches? Yes. But, such is life.
And then wakes up, with all his memories, at age 16. A gift, to go back. And change. And he has a list.
Actually learn from his uncle earlier in life
Show the Southern Water Tribe that he means them no harm and leaves them with gifts of coal and food and blankets
Join Team Avatar sooner, at the cost of his crew who either get absorbed by Zhao's crew, runs back to the fire nation, or some who stay behind to protect the tribe. His Uncle Iroh comes along with them, as Zuko and now Aang need a firebending teacher
Works to earn the repect of Sokka and Katara - eventually becoming what he considers best friends with Sokka and finds that he can learn a thing or two from helping Katara with chores about the camp
Zuko, Aang and Katara learn the bending movements of each other's elements
Zuko gives vague historical hints about Roku, that he's the great grandson of Roku, and that Aang is the reincarnation. Iroh clocks it immediately, and Zuko spills his guts over a private tea time. Zuko doesn't want to rock the boat too much, but now he sees with Iroh's eyes, that these are kids out on their own and if he doesn't know why he's come back then he'll make it his mission to help them end the war before the Comet
Lets Sokka discover swordmanship on his own, sure he nudges him, but understands Sokka has his own path
Finds that, because of his lived experiences from the first time, he isn't attracted to Mai (could end in Zutara, or perhaps even Zuko/Jin)
Gets to know Jet firsthand this time, and finds that while morally dubious is fine it serves no purpose if innocent people are harmed
Finds Toph to be like the little sister he actually wanted (big bro zuko & little sister toph time yall)
That's all i got have fun guys