If we look at HDI, religion and culture I would consider Israel not as part of the Middle-East.
Even then, it definitely is. It's Semitic, so closer to Arabic culture than Iran. It's an Abrahamic faith, it's country doesn't unyoke faith and government well at all, and it's also crap to live in (also the living standards change greatly in the Middle East - you have countries like Syria and Yemen, but also Qatar and Bahrain.).
Cyprus is partly Greek, so its Europe.
Not everyone will say this, it all hangs on who you ask.
Edited 6/26/2016 21:09:23