I can only speak from my own experience.
Last January the Mrs. and I went to Israel and biked one end to the other and all points in between over a 3 week period. I would recommend the Southern part of the country as we got rained on several days in the north. It might not be everyone's cup o'tea but the desert and mediterranean climate is pretty hard to beat that time of year. Airfare is fairly reasonable after Christmas and El Al ( Israel's national airline) carry bikes for free!
If you want route and lodging info I can point you to loads of stuff we found.
Good luck and enjoy your trip where ever it may be.
