Skerries, Portmarnock, Balbriggan and Malahide are very nice, all north of the city on the coast. Clontarf is a little further south, closer to the city.
Bettystown in Meath has an Educate Together school, and also an Irish speaking school (Gaeilscoil) that are non-denominational.
When it comes to things to do with small children, you really have to make it up for yourself in Ireland, find parks or playgrounds you like, explore the beaches, etc. There is not that much that is laid on for the very young. A lot of people invest in a nice swing/climbing set for their back gardens... There are the usual dancing (ballet and Irish) and music lessons.. If you look around, you might find horse riding.
Here's a little purple prose about Malahide:
"Malahide
Malahide is a very beautiful heritage village with old-world elegance and plenty to occupy its visitors, including Europe’s largest model railway, an exceptional kiddies' playground and miles of sandy beaches.
Cobbled side streets give the village an intimate and welcoming feel. There’s a host of chic boutiques, bookshops, and antique shops you could lose yourself in for hours. Or you could make a visit to stately 900 year-old Malahide Castle set amid 250 acres of parkland and gardens. A broad range of pubs and restaurants can take you well into the night.
If the weather is good, the Malahide to Portmarnock walk will also beckon. It’ll take you along the magnificent coastline of the northern shores of Dublin Bay where the blue flag Velvet Strand, popular with wind surfers and kite surfers, vies for the title of Dublin’s best beach."
*Maybe ask to have your thread moved to Craicnet, where you'll find lots of Irish posters.