I may be will be flamed for this, but I believe I am just being realistic. May I also point out that I
generally hate generalisations, so I am having to force myself to say the following:
Most of Northern Ireland is very pretty, and the North Coast is spectacular, but it can often still matter if you are a Protestant - CoE, Methodist, Baptist etc, or Roman Catholic. If your belief system falls into either of those religious distinctions then please do your research before you pick a town or village to live in. Most individual N.I. people are absolutely lovely, very kind, very ditsy - sorry, but they just are, and I love it, and often very funny too! But something happens to a community when it is 'overly' religious in N.I. particularly on one of the sides, but I am not going to say which - I just think you should consider the reality of the situation, when choosing where to live.
I will probably be even more flamed for this, but unless you are Welsh, and/or speak Welsh fluently, I cannot recommend Northern Wales to you. Of course there will be some lovely and welcoming Northern Welsh inhabitants, but the overwhelming feeling in shops, pubs, even their hotels, seems to be that if you are, or sound, English, you will be initially considered untrustworthy, and at least slightly hostile, and the natives will all start talking to each other in Welsh, if they weren't already when you came in.
However, I don't know if it is the same in Anglesey? I have never been there, but from the pictures I have seen of it, it is very attractive, and fairly remote, so it might be a good choice for you. Maybe, if there is a Mumsnetter who honestly knows what the general population on Anglesey is like, and how living on the Island is in reality, they could give you some helpful advice?
If you want somewhete really remote, and stunningly beautiful, then the Isle of Skye might have been made for you, but I would seriously consider renting a croft on Skye in January or February next year, before making any commitments. Oh, and you would need to be very tolerant of midges for much of the rest of the year!
Again, when it comes to being welcomed anywhere, there may be a strong likelihood of you being treated like strangers for the first 30 years or so, especially in the more remote and/or smaller places - I am of course not joking...
If I were able to move to somewhere else in the UK, my first choice would fall equally between Northern Ireland and the Highlands of Scotland. Having said that, my inner voice is screaming at me, NO, PLOCKTON, you - meaning me - want to live in or around Plockton! Plockton has the relative ease of being on the mainland, while overlooking the Isle of Skye.....