For me the biggest issue would be not be able to have one doctor/hospital follow the development throughout the pregnancy. Someone who knows the history of it and can see how things are developing. But I suppose if you make sure that you always get everything written down and carry all the medical notes with you, you should be fine wherever you go. It's great that your doctor is being so supportive!
Not sure where the best country in Europe would be. I'm from Finland, myself, and generally the healthcare there is very good, but in the recent years there have been cutbacks and longer queues etc.... But don't have personal experience of it (that goes 10 years back, and nothing to do with pregnancy & birth!).
But I suppose personally I would gravitate more towards North and West for the birth, you should be ok anywhere in those regions. I would probably not go for Southern or Eastern Europe myself.
As for giving birth from a country other than your own, I will be doing that and quite far from 'home'. We're living in China, have been for the past few years, and this is where I'll be also giving birth. I'm very, very happy with the hospital where I go to, the facilities are great and the staff are just lovely. Couldn't ask for better
