I'm becoming more interested in relocating to one of the little villages in the Carpathians in the Transylvania area, just as a retiree. Maybe renting or buying a little cottage near a small creek or brook. But I worry about not having access to medical facilities or emergency. What to do?
If you want to be near medical facilities, you would have to buy a place close to one of the larger cities in the region, namely Brasov, Sibiu, or Cluj-Napoca. The state hospitals aren't up to much so you would probably have to sign on at a private clinic for peace of mind.
Brasov and Cluj are the largest of the two. The villages around Brasov tend to be quite expensive compared to the rest of the region, probably because of Brasov residents buying weekend retreats and also because of its proximity to the Prahova valley (popular for tourism and skiing in winter) and its being on the main route to Bucharest. As a result I've noticed that typical country properties are about 25% higher in price. Brasov also has a small expat community which could be a consideration.
Sibiu is smaller than the other two and is traditionally a Saxon town. The villages in the peripheral of Sibiu county are reasonably priced.
The nicest area of Transylvania (in my opinion, at least) is the area around Sighisoara. It's right in the middle of the three cities mentioned above, and to reach one would require about a two-hour drive.
I've just seen from your other post that you are from the USA but have Romanian heritage. Do you have a Romanian passport?
If you don't, then buying a property becomes a little more complicated. You are allowed to own a house or a flat in Romania but you are not allowed to buy land. So technically, you can own the house, but not the land it's built on. For a non-EU citizen to buy land in Romania, they have to set up a company and buy the land in the company's name. This is a bit of a pain because there are costs incurred in setting up the company and even if your company does no trading you still have to pay some minimum amount of tax, plus various accounting fees and so on. You could also be liable for tax if you sell the property later on.
The other route to go down would be to get dual citizenship. If you can get a Romanian passport based on your parents' nationality, that make the whole buying process somewhat more simple - unless of course they renounced their Romanian citizenship when they left the country, then it gets very complicated again.