Women in chassidishe communities like Belz, Satmar, Viznitz, Skver, Bobov and Pupa generally do not drive.
As far as I know, the women and girls are NOT told that driving is a Tznius issue, just that it was never “oongenimen” (accepted) or “eingefirt” (instituted/introduced) by them. It seems to be a minhag that they uphold because “my mother din’t drive and her mother didn’t either….”