Leiden University has its own daycare facilities, the one near the observatory is called de Kattekop, click here for more information. Register as soon as you can, waiting lists are typically 9 months!
There is an international 'babies and bumps' group meeting in the Buurtcentrum De Pancrat in Leiden (Middelstegracht 85), suitable for pregnant women and children age 0-1.5.
Peuterspeelzaal is a morning playgroup for 2 to 4 years, which we happily recommend and is available everywhere.
homeinleiden.nl have loads more information about bringing up children in the Netherlands, check out their website!