Female travellers will generally feel as safe and comfortable as they would in any Western country. On some beaches foreign women may attract unwanted attention.
When you plan your day, keep in mind local expectations regarding modest attire. While tight-fitting, revealing outfits are common in urban centres such as Tel Aviv, they are inappropriate in more conservative areas and are likely to be met with overt hostility in ultra-Orthodox Jewish neighbourhoods such as Me'a She'arim in Jerusalem. When visiting conservative areas and when visiting all religious sites – Jewish, Muslim, Christian, Druze and Baha'i – wear clothing that covers your knees and shoulders. In Muslim and Christian areas, long trousers are OK, but in some Jewish areas – and at all Jewish holy sites – only a long skirt is acceptable.
It’s a good idea to carry a shawl or scarf with you at all times. You will need this to cover your head and shoulders when visiting Muslim holy sites (mosques, tombs and Temple Mount/Al Haram Ash Sharif), and it can come in handy if your definition of modest attire doesn’t align with that of the caretaker in charge of a religious site.
In buses and sheruts, a woman sitting next to an ultra-Orthodox Jewish man may make him uncomfortable. Depending on how you look at it, that's either his problem or a local sensitivity you should respect.