Most towns / cities are absolutely safe….even when you are out late into the night. You can easily walk a lot & use public transport. Carry a good map / guide-book with you. Also carry your hotel address & phone number at all times. In fact, it is a good idea to ask your hotel staff to write down both these details for you, in Arabic, as it helps if you have to get directions from people who cannot read English.
Pick up a local SIM card for your mobile as soon as you reach Egypt…..it helps to make calls to your hotel / guide, as there are no coin operated public phones available. You need to get a calling card for these phones, but, in any case, these phones are hard to come by.