baby nursery; day nursery; crèche
A facility where babies and very young children are cared for during the day; similar to a day nursery or crèche. The gloss 'baby-farm' is dated and potentially derogatory; modern usage corresponds to a nursery or childcare center.
She leaves her child at the day nursery while she works.
託児所 is a more general term for a childcare facility, often temporary or drop-in, whereas 育児園 implies a more regular, institutional setting for babies.
Compound of 育児 (ikuji, 'childcare') and 園 (en, 'garden, facility'). The term is transparently derived from its components.