Disclaimer: 'Avatar: the Last Airbender' is not mine
A/N: Teaching seems to me like a natural choice for Toph, but not one that she is likely to come to easily. Here's my idea of how things might have worked out.
Ozai was defeated and the war was finally over. That business taken care of, Toph was ready for the fun to really start. She anticipated all the benefits of friends and freedom she had grown to love, without the inconvenience of being constantly on the run, and for the first few weeks, that was how it was. But once things had settled down some, everyone else became so serious. Aang, Zuko, and even Sokka spent all their time in important meetings that bored Toph to tears. So it was with some regret, that she left her friends to travel the Earth Kingdom on her own.
Toph received a hero's welcome in the first town she visited. It turns out that being the avatar's earthbending teacher had some benefits. People crowded the streets to get a look at her, their shouts deafening. Stone slabs were shoved in front of her along with requests for autographs, and these Toph happily obliged, stamping images of her likeness into the stone. Eventually the mayor himself appeared and asked Toph if she might provide them with a demonstration of fighting prowess. Toph broke into a savage grin. "I thought you'd never ask."
Toph waited, smiling as the crowed gathered in the hastily erected arena. The announcer droned on, stalling for time by introducing the soldiers and hotheads who had agreed to face her. It was with some regret that Toph realized that she wouldn't be fighting as the Blind Bandit anymore. That moniker had served her well, but Toph Beifong was now better known than that brawler had ever been. Finally the announcer finished, and Toph got ready. It had been a while since she'd had a real fight.
Round 1- A boulder distracted her opponent, while a column erupting under his left foot sent him sprawling. He was easily thrown out of the ring.
Round 2- Toph's opponent quickly took the initiative, launching a rock at her head. His great lunge forward betrayed his intentions though, and the attack was easily sidestepped. Toph made a small, circular motion with her leg, and her opponent found that the solid ground he hoped to step on had turned to sand. A rock rose to meet his head as he fell, leaving him out cold.
Round 3- The announcer had barely finished speaking when Toph found herself faced with an oncoming wall of earth. She dove through its center, emerging armored on the other side. Contact was reestablished with the ground, and its vibrations revealed Toph's opponent barreling towards her. A quick kick launched Toph's stone boot at her opponent. It was soon followed by its mate and a pair of gauntlets. Toph's foe managed to swat two of the projectiles aside, but one of the gloves grazed his shoulder, and then a boot to the knee sent him tumbling. Toph sidestepped the incoming pile of muscle, and with a flick of her hand sent him sailing out of the ring.
Toph shed her remaining armor, and was surprised to find the announcer lifting her arm high and announcing the end of the match. As the deafening crowd began to rush towards her, Toph grinned despite a stab of disappointment. "Don't worry" she thought, "this is just a small village. Elsewhere you will find opponents worth facing."
So Toph continued her tour of the Earth Kingdom. She continued to fight to the cheers of roaring fans. But as time went on a quieter, more deliberate group joined those following her. This new group stayed in the background as if studying her. This behavior puzzled Toph until she confronted them about it. "Sifu Toph," said one, acting as their leader, "we have witnessed your mastery of earthbending and wish to learn from you. Would you instruct us?" Toph snorted in reply. "Do I look like your nursemaid? I have better things to do than to babysit a bunch of novices." The group dispersed, but Toph suspected that she had not seen the last of their kind.
After a dozen towns and scores of matches, Toph was still unsatisfied. The earthbenders she met seemed to think that their strength came from huge muscles and dramatic lunges. Their flailings left them unbalanced and vulnerable to Toph's swift, precise attacks. As Toph's dissatisfaction grew, she searched for new ways to make the fights challenging. She fought multiple opponents or with her arms bound, some idiot even suggested that she try fighting blindfolded. But although these gimmicks make her fights more dramatic, they failed to make them challenging.
The beginning of the end of Toph's career as a brawler came from a simple fight in an arena in Ba Sing Se. Toph faced a single opponent, having already dispatched his teammates. The young man stood motionless on the other side of the ring. The deafening roar of the crowd hampered her ability to track her foe. Finally locating him, Toph launched a boulder at him, but rather than deflect it, her opponent started running. He kept moving, and showed surprising agility for an earthbender as he dodged Toph's onslaught. Although Toph eventually defeated him by way of collapsing half the arena, she had little satisfaction from it.
That night Toph sat picking her feet on the street. The months had dulled the shock of the war's end, and as people moved on with their lives, Toph's fans began to disappear. She was still plagued by would-be disciples, but they largely lurked in the background, and so she was alone. She was listening to the celebrations in the tavern across the street. Toph's opponent was being praised for his pathetic performance since his cowardly display had allowed him to last almost a minute against the "tiny terror".
Toph was preparing to leave when she felt footsteps approaching. Toph stood as a gangly young man approached her. "What do you want?" asked Toph with some annoyance. "Sifu Toph" he said, "I wish to learn earthbending from you. My name is Kett and-". Toph grabbed his collar and pulled him down to her height. "I don't care what your name is. Unless it's 'Aang', and you happen to be the avatar, I'm not teaching you." Toph threw Kett to the ground and called back to him as she stomped off "But of course it's not. Not even Twinkletoes is that scrawny."
By the next day, word of her delayed victory had spread. Her matches in the ring changed character entirely as the opposition gave up all pretense of trying to win and instead opted to try dancing around in order to evade her fury as long as possible. The crowd seemed to enjoy the new dynamic, and despite her best taunts, Toph could not get her foes to stand and fight. By her fourth match, Toph was thoroughly annoyed. A single opponent came from the stands and knelt before her on the stone ring. "Is this some strange stalling tactic?" asked Toph. "Stand up so I can kick your sorry ass out of here." "Please" the man replied "I wish to learn from you." Finally recognizing him from the previous night, Toph answered "You wish to learn? Fine." A column of earth smacked into Kett's stomach, sending him flying "Lesson one: the ring is for fighting." With that, Toph strode out of the arena.
Finally fed up with the way things had been going, Toph left Ba Sing Se. Lacking another destination, she found her footsteps leading her slowly back to Gaoling. At least dealing with her parents would give her something to do. She took the odd fight as she traveled, hoping that somewhere would be a foe worthy of her skill. It was not long until she met Kett in the ring again. This time she recognized him immediately. "Hey shrimp" she said, "I told you, school's out. Stop following me." Kett bowed in response "Sifu, I have thought upon the wisdom you imparted to me last time." Toph laughed at this "Sure, I'm just full of deep wisdom. How do you like my long, grey beard?" Toph's laughter stopped abruptly as she noticed her opponent had begun advancing, swinging his arms to launch rocks at her head. Toph raised her fist to shatter the first rock, and batted the second aside. She dropped to her hands to duck the third, and as she pushed herself up, the ground underneath Kett collapsed in an avalanche. "Lesson two" Toph laughed, "Watch your footing."
Kett caught up with her on the road the next day. He followed her at a distance for some time until Toph doubled back to confront him. "What is wrong with you?" she demanded, "Get it through that thick skull of yours that I'm not going to teach you. Leave me alone." "Please" Kett replied "I want to learn from you. I can pay for lessons." With a snort, Toph turned to leave. Toph could hear a hint of desperation in Kett's voice as he called after her "Please" he said "one more fight and then I swear I'll leave." Toph stopped. "Fine." She turned and raised her arms, lifting a ring out of the ground. "This shouldn't take long."
Toph faced Kett from the other end of the newly raised battleground. She prepared her stance as she waited for him to be ready. From the other end, Kett bowed briefly before launching his attack. A boulder flew at Toph, but was easily deflected. As the second came, Toph noted that her opponent's movements were more solid than last time they had faced. While considering the most amusing way to end this fight, Toph was startled as the ground began to slide beneath her feet. She dropped a hand to the earth in order to stabilize it, and rose with a grin. Kett's attacks continued at an unvaried pace. Toph deflected another two boulders, and then between his strikes, launched a spike of rock hitting him squarely in the chest. Kett was knocked off his feet and began to slide out of the ring.
As she felt Kett tumble towards the edge, Toph relived the disappointment of every anticlimactic fight she had fought in the last months. "If only he could have been more of a challenge" she thought. As Kett flew out of the ring and disappeared from Toph's perception, she could almost feel her future vanishing with him. The sad state of earthbending would leave her singularly alone. She would spend her life being praised simply for being better than her glaringly incompetent peers. In this era of peace she would never again find a worthy adversary. With such a path ahead of her, she might as well just go home.
"No!" Toph yelled, as her hand darted forward. An outcropping of rock sprouted from the edge of the ring, catching Kett and dragging him back in. Toph laughed as Kett stumbled, confused to his feet. "Lesson three" she yelled "wait for the right time to strike." Stable once more, Kett threw another boulder at Toph. Toph raised a wall, and grinned as Kett's rock smashed upon it with a great boom. Kett continued his assault with ever increasing ferocity, but Toph's defenses held. "Lesson four" said Toph, making a twisting motion with her hands "earth is more than a bunch of rocks." With that the ground beneath Kett's feet began to tilt. Halting his attacks, Kett managed to maintain his footing, but was soon sent flying as a slab that once been a side of Toph's wall plowed into him.
Toph caught her opponent before he could leave the ring, and dragged him back to the center. Toph shook the field sending a cloud of dust into the air. "Lesson five" she said "listen." Kett paced around warily in the cloud as Toph stalked slowly towards him. As the seconds wore on, Kett grew increasingly nervous. Eventually he heard a sound, and launched a rock in its direction. As his attack sailed harmlessly through the air, Toph emerged from the dust delivering a punch to the gut and knee to the back of the leg, sending him to the ground. Kett let out a grunt as Toph delivered a final stomp to his stomach before stepping back. "Please, no more. You win" he pleaded. "Not a chance" said Toph, "I'm going to make you into an earthbender worthy of the title if it kills you." A twist of her hands created pillars, dragging Kett to his feet. "Lesson six" said Toph with a grin "don't give up. Ever. Now show me what you've got."