El Alamein — 120 km west of Alexandria is the site of several important battles from history and currently home to a number of war memorials, cemeteries and museums. Also built on the Mediterranean coast, El Alamein was once famously described by Churchill as having the 'best climate in the world'.
Marina — upmarket beachside resort about 100 km from Alexandria
Jordan is accessible via inexpensive for the region flights via discount carrier Air Arabia. They don't fly from Cairo, so this seemingly would be the only discount route flying between the two nations.
