First, can I just say, JEALOUS!! (And that doesn't look like the center of Athens to me, )
Is that whole long strip in the 2nd pic, the backyard? Bougainvillea is everywhere there, and beautiful, but if kids are running around playing it definitely needs to be up high, as Rita suggested. A pergola would be lovely. Lots of succulents will work here.
Some beautiful ideas here...
https://www.pinterest.com/nishatfatima125/patio/?lp=true
Q