Did you forget about Kya? Everyone forgets about Kya.
Industrialization has shrunk the world. A few days by boat will get you from the Southern Water Tribe to Republic City. Travel by airship, Air Bison, or aeroplane and you can cut that time to hours. Travel by Spirit Gate and you can be there in minutes.
Katara has already had an adventure of SEVERAL lifetimes, both with Aang as the Last Airbender and afterwards with the founding of Republic City. She's lived around the world, with a tight knit group of friends and family, in the bustling urban city. Once Aang is gone and the kids are grown up and out, the family is already separated (Bumi with the Navy, Tenzin at the Air Temple, Aang passed away) it is literally impossible to all live together without being manipulative and controlling.
Her kids are living their lives so she lives hers in back where she grew up along with her daughter Kya, passing on their ways, their culture, their skills to the people most equipped to receive them. If and when she misses the rest of her family she can always write, telegraph, record a mover, or travel by the aforementioned means.
In short, the Southern Water Tribe is where she is most at home, can contribute the most, is least out-of-water (no pun intended), least intrusive upon the lives of her children pursuing other cultures and careers, and still able to maintain contact by communication or travel.