ATMs, widely available at airports, hotels, and throughout major cities, are generally the most straightforward and reliable way to get Egyptian pounds, typically at a reasonable exchange rate without needing to seek out a specific exchange counter.
Banks, official counters, and what to avoid
Bank branches and official currency exchange counters are a solid alternative for exchanging larger amounts of foreign cash, and are generally more transparent about rates than informal street-level exchange, which is best avoided entirely.
Airport exchange counters tend to offer less favorable rates than ATMs or in-city banks, so it's generally better to withdraw only a small amount on arrival for immediate needs (a taxi, initial tips) and handle the bulk of your currency needs once settled in the city — all monument ticket prices are set in EGP (per official government sources), and self-service machines at Giza specifically accept bank cards directly, a useful exception to the general cash-first pattern.
See What Currency Should You Use in Egypt? for how EGP and foreign cash typically get split across a trip.