Until you nominate the country to which you want to move you might as well be asking (with respect) How Long is a Piece of String? Even countries in the EU have residence/tax laws which differ from country to country. I still pay taxes in Ireland although I spend up to eight months out of the country in any twelve month period. We own an apartment in Spain and rent a place for a few weeks in both France and Italy.
Approaching retirement isn't the most efficient time to think about uprooting yourself and perhaps your wife. However, it is what it is and the OP appears to be the kind of person who'll take lots here onboard. Here's my unexpurgated solid advice which I've given to many:-
1. Compile a SWOT analysis of your situation (Strengths, Weaknesses Opportunities, Threats).
2. Choose the country where you want to live.
3. Choose the area in that country.
4. Rent a property there for a few weeks over the cold months (forget about a fortnight's holiday for some recce). Living abroad for over six weeks ain't a holiday it's a change of lifestyle.
5. Use the off period rental to ask questions on local forums, people with whom you meet, even the local chancer or better again Bob-down-the-pub. Unlike me, people are usually sympathetic with such advice - I'm pretty cold, but wouldn't knowingly steer you in any wrong direction.
6. You wish to keep your house in Ireland (good decision) so your foremost thought is succession rights. Likely, you've made a will in Ireland, so you likely will have to make another will (in tandem with your Irish will) in your new country.
7. In your 60's I think buying property abroad is a bad move; I suggest you rent a place suitable to your needs. If you rent out your Irish property you should end up financially better off covering your expenses abroad. But, sin scéal eile looking at some Landlord/Rental threads on this forum.
8. Here's a titbit if Spain could be your choice - spend six months there ( 183 days, January - December) and you will be liable to pay income tax in Spain on your worldly income and how do you know they'll implement this - You will when they present you with the tax bill on printed paper and in black and white. Now you know why I spend 180 days only in Spain.
Later Add On:- If you have any tax free investments in Ireland, likely they'll not be tax free in Spain - not many know this and many's a "tax-free" nest-egg became a faller here.