Israelis dress very informally and Palestinians tend to dress up a bit more; most international tourists dress informally. It is unacceptable to wear short shorts or halter tops in conservative Palestinian or Israeli areas, including the Old City of Jerusalem. In touring, pants are acceptable for women unless they are too tight; skirts are acceptable unless they are too mini. Women do not have to wear long skirts but if you are visiting religious sites it is a good idea to carry a light weight scarf and wear short or long sleeves (no sleeveless shirts or halters). If you are visiting ultra Orthodox Jewish areas, women must wear long skirts and long sleeve blouses. Slacks are prohibited. The Mediterranean beaches and Eilat are generally “anything goes” territory.
Men can dress in open neck shirts or pullover shirts and slacks but bring along one necktie for a special occasion. Men who wear shorts at religious sites are often given a skirt to wear over them. Men will need to wear a head covering in Jewish religious areas such as synagogues. The area closest to the Western Wall is an outdoor synagogue but men can obtain paper yarmulkes (kipot) at the entrance.
Sandals with bare feet are appropriate for both sexes even in religious locations. In the winter you will see sandals with socks on many feet. Since there is stone paving, the best solution is good sturdy shoes with socks for everybody.