Egyptians are generally a conservative people and most are religious (roughly 90% Muslim and 10% Christian) and dress very conservatively. Although they accommodate foreigners being dressed a lot more skimpily, it is prudent not dress provocatively, if only to avoid having people stare at you. It is best to wear pants or jeans instead of shorts as only tourists wear these. In modern nightclubs, restaurants, hotels and bars in Cairo, Alexandria and other tourist destinations you'll find the dress code to be much less restrictive. Official or social functions and smart restaurants usually require more formal wear.
At the Giza Pyramids and other such places during the hot summer months, short sleeve tops and even sleeveless tops are acceptable for women (especially when traveling with a tour group). Though you should carry a scarf or something to cover up more while traveling to/from the tourist destination. Also, it's perfectly acceptable for women to wear sandals during the summer, and you will even see some women with the hijab who have sandals on.
Women should cover their arms and legs if travelling alone, and covering your hair may help to keep away unwanted attention. Though as a foreigner, you may get plenty of attention no matter what you wear, mainly including people staring at you along with some verbal harassment which you can try to ignore. Egyptian women, even those who wear the full hijab, are often subjected to sexual harassment, including cat calls. You may find that completely covering up does not make a huge difference, with regards to harassment, versus wearing a top with shorter sleeves. In regards to harassment, it's also important how you act. Going out with a group of people is also helpful, and the best thing to do is ignore men who give you unwanted attention. They want to get some reaction out of you. Also, one sign of respect is to use the Arabic greeting, "Asalamualaikum" (means "hello, peace be upon you"), and the other person should reply "Walaikumasalam" ("peace be upon you"). That lets the person know you want respect, and nothing else.