going away for a month at a time

Following a recent health scare DH has suggested having longer holidays abroad. I am worried about hospitals etc. and will we no longer be eligible for free treatment in Europe. Our favourite place in Greece is two hours away from the nearest hospital and we have heard really bad reports on the treatment and cleanliness there. I know we would have travel insurance and if we went on a package holiday a rep to sort things out if necessary. Trouble is, we prefer to make our own way - booking flights and accommodation independently. I would really appreciate your thoughts and suggestions of places to go. A bit of winter sun would be lovely.