Thanks to Kenichi's arrangement, the girls ended up working at various places around town.
Literal
They [topic-は], Kenichi [possessive-の] arrangement [with-で], town [possessive-の] various places [at-で] work [decided-ことになった].
はからい (計らい, 'arrangement, good offices') is a slightly formal/literary word for someone making things happen behind the scenes. 町の様々な場所で ('at various places in town') is the location. ~ことになった ('it came about that') describes an outcome resulting from external arrangement rather than personal decision — contrasting with ~ことにした. 彼女たち uses ~たち as the pluralizer.