Recently I had the chance to visit the Azores islands. Well actually only one of them actually (the largest one Sao Miguel)
This rather remote location in the middle of the atlantic ocean, approximately half way between Europe and American is a great place for motorcycling.
There are many mountain roads, beautiful views and fantastic nature to look at, oh and did I mention the riding is great!
There are many twisty mountain roads that unlike mainland Europe have not been damaged by cold weather (freeze/thaw effect) and the temperature is between around 17c and 25c all year round.
Couple that with friendly locals and good prices (compared to other similar destinations) and this a very nice place for a biking holiday.
The main drawback is that it is almost impossible to travel there with your own motorcycle but I saw a company renting Honda CB500x bikes from ponto delgarda and here is a link to their site.