In The Legend of Korra, the lives of the original cast from Avatar: The Last Airbender get explored in some detail. Toph actually features more than most of the other original characters other than Katara and Aang. However, the issue of her romantic life is still a bit of a mystery.
While she does have two daughters with two different men, it’s never really explained in the show who these men were or the nature of their relationship. However, there are many characters from the series that would have been a good match for Toph.
Zuko
While Zuko doesn't seem to ever have much interest in Toph, which makes sense given he's older than her doing the events of the story, Toph has a bit of a crush on him.
She wants to go on a solo adventure with him like the other members of Team Avatar get to, and she even clings to him a little bit. While these two probably would have become good friends over the years, they don't seem like the best match even if Toph did have a crush on him.
Katara
Katara and Toph often don’t get along because they have very different personalities. Katara can be too controlling while Toph can be too reckless. Of course, as they grew older, these differences could have evened out somewhat.
They clearly would have known each other quite well and been friends for years, so while they aren’t the most perfect fit personality-wise, they might work together romantically given their friendship.
The Duke
This inclusion on this list, as well as many others, comes with the caveat that all of these relationships would only occur once the characters were older. In The Last Airbender, Toph is really young, and so are many of the other characters.
However, The Duke is an adorable freedom fighter who is briefly part of Team Avatar. While we don’t know much about his later life, these two seem like they could have at least been friends.
Smellerbee
Smellerbee is another Freedom Fighter who eventually becomes the leader of this group, and while these two don’t have a lot of one-on-one interactions, they actually seem like they would get along well. They are both fierce and strong characters who aren’t the stereotypical character based on their gender.
They would likely relate to the fact that people tend to underestimate them, and their personalities seem pretty complementary even if they aren’t that close in the canon.
Suki
While Toph seems to have more of a crush on Sokka in canon, she seems to get along well with Suki, too. While Suki isn’t always a part of Team Avatar, she does feature rather often, and she even rescues Toph one time.
Toph has a more forceful personality, but Suki is also able to hold her ground and is quite determined. Because of these personality traits, these two would probably get along pretty well.
Satoru
Satoru is actually a character that Toph does almost date, but many fans might not know about this as it happens in the comics. Satoru works at the Earthen Fire Refinery that his uncle owns, and he sees Toph as a bit of a celebrity.
While these two seemed to like each other a lot, Toph loses respect for him eventually when he doesn’t stand up to his uncle. However, these two could have been together more long-term even if this didn’t happen in the canon.
Aang
Aang and Toph would make for an interesting pairing because they are opposites in many ways. Toph is a tough earth bender who isn’t particularly emotional while Aang is a more gentle soul who is most connected to air bending.
While these two don’t get along at first, they do become close friends and allies throughout the years. There is also a fairly strong shipping fandom surrounding these two characters.
Sokka
Of all the characters that Toph often gets shipped with, Sokka is probably the most popular. Despite the fact that these two didn’t ever have a canon relationship, many fans feel they could be a good fit, and there is even some speculation that Sokka fathered one of Toph’s children.
Toph always had a crush on Sokka, and they got along well. Because of this, they would be a pretty good match.
Kanto
This is the only person on this list that Toph is confirmed to have a long-term relationship with. However, there isn’t much information about him or their relationship.
Toph only ever reveals that he’s the father of one of her children and he was a “nice man.” Her own daughters never even learned anything about him. The whole situation is very secretive, but she at least liked him enough to be with him long enough to have a child.
No One
While there’s a tendency in fandoms to want every character to have a romantic relationship and often with another main character on the show, there’s no real reason why Toph would have to be with anybody especially for any serious relationship.
Overall, Toph is a strong personality who is very independent and doesn't like to be tied down. Because of this, it makes sense why she might not date people for very long.