For a 10-day excursion in Israel, here is a possible itinerary, based first in Tel Aviv and then in Eilat on the Red Sea. From Tel Aviv, explore Tel Aviv itself, including the old port of Jaffa. Then drive north to the Roman ruins of Caesarea and east to Galilee, stopping at Nazareth. On another day proceed east from Tel Aviv to the Ayalon Institute and the Sorek Caves. Then visit Jerusalem for a day, starting on the Mount of Olives. Then change your base to Eilat and stop at the mountain fortress of Masada and the Dead Sea on the way. In Eilat, enjoy the Red Sea and travel to the Petra ruins in Jordan. For a final day, traverse the Negev Desert, seeing the science intellectual center Be'er Sheva.