In the Legend of Korra we find out that Toph moved to the swamp alone and has been there for some time. Is there any explanation, definitively or implied, as to why she moved there?
In one of the episodes she's talking about how in the Swamp there's a ton of mud, trees, rock, basically a ton of earth. She also talks about how the trees in the swamps have roots that spread all over the earth. She can literally see cities and people using her Earth-Bending.
From Season 4 Episode 3 "The Coronation" as Korra is training with Beifong, she actually asks that exact question"
So, what made you wanna drop out and disconnect from the rest of the world?
I'm more connected to the world than you've ever been! The roots and vines...they run all over the world! I can see Su and Lin, Zao Fu, and Republic City....I see EVERYTHING. Korra tries to attack from behind You're blind compared to me!
She's in The Swamp because it's where she can use her Earth-Bending to her maximum and also see everything at the same time.
"Toph eventually set out to roam the world in search of enlightenment before settling down in the Foggy Swamp." - https://avatar.fandom.com/wiki/Toph_Beifong