I have just spent a week in the Paphos area and was very pleasantly surprised by the quality of the cycling on offer in the area. Good quality roads, big hills (all the way up to HC climbs), great views and very little traffic in the mountains. The only problem was the heat but I believe the best conditions are from October through March.
I hired a Boardman road bike through this company (Don't be put off by the name):


Al Yates was very helpful and can help with routes, group rides and support if required. He told me he could arrange off season accommodation for as little as 100 euros per person a week.

The only downside to cycling this time of the year there is the heat - I had to be out at dawn and heading home around 9am or else I would start to melt ! Then again, I was only cycling to keep the legs turning over in preparation for the ride100 but I would consider it as an off season destination based on the week I spent there..