If you like hiking, do the Inca trail from Cuzco to Macchu Picchu. Takes 4 days and is exhausting but the scenery is spectacular. You need to go with a tour company because access to the trail is limited. The company provides porters who carry everything, set up tents, cook, etc. Peru is only about a 6 hour direct flight from LA.
The Greek islands are also beautiful. We went hiking on Tinos, Mykonos and Santorini last year. Near to our hotel in Mykonos there was a bar called "The Ramrod," not that there is anything wrong with it ...
This summer we are going to hike in the Carpathian Mountains of Romania. Always wanted to see Dracula's castles.
If you really are worried about terrorists, there have been recent attacks on Turkish tourist areas by Kurdish separatists ... but you are probably still safer there than in LA.
