Taxis fares in Greece are Government controlled and reasonably cheap although there is nothing to stop you haggling. Do not be concerned if your taxi picks up another fare on the road. This is customary and the fare should be shared - although drivers will often try to rip tourists off on the more popular islands like Rhodes. Many islands have a health centre despite their small size. Young trainee doctors are often posted there for our equivalent of an intern year and are usually very good and, most importantly, often speak excellent English - so you can explain what is wrong without an embarassing pantomime performance.
Pharmacies are also a good place to visit for common ailments.
Pharmacists in Greece are very often highly trained and can offer good medical help and advice for free - unlike assistants in British chemists who always seem to me at least one pill short of a party. Care in Greek hospitals has much improved in recent years and is now generally very good too. But note that nurses will only perform medical duties - they will not look after you as the proverbial angels do in British hospitals. On the islands, of course, you won't get to a hospital without a boat trip.