is safe to travel in the middle east ?

If you have a legal passport, then, why not? Yes.

Depends on where you're off to. Try avoiding the chaotic countries (Iraq, Iran, Syria, Yemen). There's a federal travel warning on countries that is updated, please visit http://www.travel.state.gov/travel/cis_pa_tw/tw/tw_1764.html

I have been to UAE, and Kuwait. Dubai is fabulous. Try it.

Greece isn't the middle east.