Koichi, look...
For japanese people it's no problem at all. Special for _YOU_ I can get some days of vacation on my work, and we can travel on my car for all of the country: Dead Sea, Jerusalem, Jaffo, Acco – where you want. You just should care about your place of stay for night. I have a small apartment and can't give you a room for living.
About your Egyptian friend... It's not so simple. As you know, most of Arab and Muslim countries isn't friendly to Israel. Egypt and Jordan cureently have like "neutral" status, but it can't be called "friendly".