A police station was no place for a six-year-old; even Lin recognised that fact. Then again, she wasn't a normal little girl.
The people were nicer than those at her school. Just because she didn't have a father didn't mean she was unsophisticated (a fact she disputed by earthbending the perpetrator onto the roof).
At the station, she often wandered around, talking to the officers; they were entertaining, and it meant she could spend more time near Toph. Plus, sometimes they asked her to calm down a victim.
She needed–and wanted–to help everyone.