Petra, meaning stone, is an ancient city in Jordan chiseled of stone. Don't bring the children until they are old enough to appreciate it and hike it on their own. Established as early as 312 BC, today it is a UNESCO World Heritage Site. Its called the Rose City after its reddish mountains. The buildings are half-built, half-carved into the mountains' sides. The city was lost until the mid-1800s when archaeologists re-discovered its splendor. You'll recognize it from the Indiana Jones movies.
At its pinnacle is a Monastery, 804 uneven steps straight up, it will take you more than hour to climb, but from there you'll have one of the best views in the world.