Have a look at a map of Dublin. The river Liffey cuts Dublin in half - northside and southside. The northside might be convenient if you'd like access to Dublin airport. as it's on the northside of Dublin. The southside offers easy access to county Wicklow, which has some really stunning mountain scenery (Wicklow Mountains National Park).
The coastal areas of Dublin are the most popular, for obvious reasons - who wouldn't like to live by the sea? And the coast is served by the DART rail line. @maftaz has already listed some very desirable areas. But of course, you'll be paying a premium price to buy a house in these areas. Which is why I said, "If money is no object.....". I'd need to win the Lotto to pay for a house in those areas
. If you can't afford to buy in those areas, there are some nice leafy suburbs further inland. I don't know the northside so well, but on the southside you have areas like Ranelagh, Rathgar, Rathmines, Terenure, Templeogue, Rathfarnham, Dundrum etc. A lot of these areas started off as villages and then the city grew out and engulfed them. Houses are very expensive in these areas also, because, you know, leafy suburbs.
If you can't afford to buy in Dublin at all, then you'd have to consider commuter towns outside of Dublin, in adjacent counties like Wicklow (south of Dublin), Kildare (south west of Dublin), Meath (north west of Dublin) and Louth (north of Dublin). As I said, traffic in Dublin is chronic, so if you're considering a move outside of Dublin, then I'd choose a commuter town with a rail connection to Dublin. A lot of Dubliners have moved out of Dublin in recent years, because they've been priced out of the capital. So that has resulted in an increase in house prices in dormitory towns and has also put pressure on schools in adjacent counties. Would your DH have to travel to work five days a week, or is working from home an option? If he can work from home (even part of the week), that would make a long commute easier.
When I was talking about schools, I forgot to say that our school holidays are a lot longer than in the UK. The primary schools close for two months in the summer - July and August. The secondary schools close for three months in the summer - June, July and August. State exams take place in June. I know you don't live in the UK at present, so I don't know how this compares with your current country of residence. It's great if you're a teacher (I'm not), but not so great if you have to arrange (and pay for) childcare for that length of time. And even if you're a SAHM, it's a long time to keep kids entertained, especially if we have a rainy summer. We sort of take it for granted, because we grew up with it. And I have to say, I loved the long summer holidays as a kid myself. However, I'm amused when I read the lamenting and handwringing on MN about the six week summer break in the UK.