North Coast jumps to mind immediately. I'd live in Portstewart in a heartbeat if I could. We're in Jordanstown, just north of Belfast on the coast which is probably too close to the city for you. I honestly think few areas in Northern Ireland would be a problem these days. The main thing, I would imagine, is work opportunities?
Portstewart is lovely but very built up. It's good if you want cafes, pubs, restaurants all within walking distance, and it's just down the road from Coleraine, with sainsbury, M&S, leisure centre, etc.
If you want less built up, more rural, wild and scenic, Ballycastle might be an option. It's a smaller town, yet with all the amenities, and the surrounding scenery is stunning.
I used to work in Ballycastle, it’s a lovely place with lots of amenities. You are looking at a bus to Coleraine/ Ballymoney for a choice of post primary schools, and it is quite a long way off the main road. That said, nowhere in the north is really that far from anywhere not by driving-in-England standards. If you want North Coast, villagey, you could look at Castlerock, Portballintrae and Bushmills too. All in that general Coleraine area, lovely beaches, interesting weather. A bit further inland, but still very handy for the coast, are Limavady, Kilrea and Garvagh - small towns, lots of rural living in the areas around them. If you are used to house prices in England you will find you get a whole lot of house for your money over here. Maybe research the internet situation though, if your job relies on it. I live in the hills surrounding one of the aforementioned towns, and I have to encourage some very patchy broadband into my house via a satellite dish and many swear words.
North coast springs to mind from me as well - Portrush, Portstewart or Castlerock. All within easy reach of Coleraine and good travel links to Belfast or Derry. Schools are excellent with a good range to choose from - both at primary and secondary. English accents aren't out of place around here due to being a university town and being a tourist area.
Or what about South Down - Newcastle, Annalong, Dundrum round to Ardglass, Strangford or Killyleagh?
I was born and raised in Newcastle and would be back there like a shot if circumstances permitted - currently up on the north coast.
Holywood or Bangor. Handy for commuting to Belfast if the type of job you do needs to be there but both are beside the sea and Holywood especially has a fairly good community and loads of ex pats from all over.
Pretty much all our schools are great. I'm inland County ANTRIM but still just 25 minutes from the coast & the City. It's a great place to live but even though it's my home, having lived away for 15 years I've found it hard to integrate back, although there is a good community feel in most areas. I'd just say avoid Carrickfergus. For some reason, that seems to be where the weird folk go.
If you go soon you could meet a batch of baby ladies for the new baby. I know you say you are atheist but most of the good mum & tots are held in churches so think if you're happy to attend these as there's not as much sure start etc
Crawfordsburn and Helen's Bay are lovely, Helen's Bay has the train station, C'burn the shop and garage, and the C'burn Inn-which is good for a drink but don't believe the hype about the food, it's not good. C'burn country park is lovely, we go there often. I have plenty of lovely friends in both areas who really rate them. Bangor, well, it's a bit of a dump, like so many sea side places it has an air of neglect about it. I know people who live here and one is hoping to move back to Belfast she feels 'forgotten' out there, they other stays for family nearby. You'll get more for your money here though.
Depends where you move to in Bangor, it's a bit mixed. You'll be able to tell by looking at the house prices. Groomsport might be worth looking at and if Helen's Bay is in your price range, then Cultra too.