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Cairo has only two seasons: summer and 'not-summer'. Given the choice, you're far better off visiting during 'not-summer', a period that stretches roughly from September to April or May.
It's also worth considering the timing of the various Muslim festivals when planning your trip. During Ramadan, the Islamic month of fasting, many businesses work half-days, museums and tourist sites shut early and many restaurants only open after sundown. Alcohol is rarely served outside hotels and you may have to show a passport to prove that you're not Egyptian (they're forbidden from drinking in public places throughout the month).
