I (female) visited these countries with a friend on a tour 5 years ago. We never once felt in danger or threatened and as Marmora Man said, the locals are among the most welcoming and friendly people you'll encounter anywhere in the world. I would second everything in Marmora Man's post, and also add Wadi Rum, Petra and the Dead Sea in Jordan as great places to visit. Camp overnight in Wadi Rum if you can, and jump the fence to get in to Petra at dawn to see it at its magical, deserted best. The main advantage of travelling with a tour (having compared experiences with friends who did it alone) is ease and speed of getting from place to place, especially with border crossings, which is an important consideration seeing you only have two weeks. We went with On the Go which is great if you are not the sort of people who would normally do an organised tour. They just make sure you get from A to B safely, and the rest is up to you. It's quite basic though - camping on a lot of the nights. Have an amazing time - it's a fabulous part of the world.