Egypt

To start I would pick up the latest Lonely Planet Egypt Guide book
https://www.lonelyplanet.com/egypt#guidebook

Most hotels will be able to arrange excursions. Our hotel arranged our trip a sleeper car train to Luxor and then to Aswan and then a day trip all the way to Abu Simbel. A random cab driver arranged our trip to the Pyramids where we rented camels to tour; but I would not suggest you try that approach.

Alexandria for the day, or several days?
I took a Trafalgar tour shortly after Arab spring. It was a Nile cruise with Cairo. As it didn't visit Alexandria, I arrived 2 days early and hired a,local woman guide for a long day trip to Alexandria. Next day hired her driver to take me to Pyramids and wander with me. He wasn't quite the touts deterrent I had hoped he would be, but it worked out.
I hired her from Tours by Locals website. Her name is Rasha Eleshmawy. Still guiding and getting good reviews.
I remember RS info on Egypt. I also reviewed ot for consideration....before Arab Spring.

It looks like Lonely Planet's current book came out in July, 2015 and the next one is expected this July, if you can wait that long.

Rick's posts from 2013 are collected here.

this is a tour program for cairo and alexandria;
Day 01
Visit to Sakkara and Memphis.
continue your tour visiting the Great Pyramids of Giza and the Sphinx

Day 02
Visit to the Egyptian Museum.
Then continue to the Citadel of Salah El-Din and Mohamed Ali Mosque.
dinner Cruise of the Nile River

CAIRO / ALEXANDRIA
Day 03
travel to Alexandria by bus (220 km).
Arrive Alexandria and start your tour visiting;
The Pompey's Pillar and the Catacombs of Kom El-Shoqafa.
visit to El-Montazah Garden.

ALEXANDRIA / CAIRO
Day 04
¯ Check out after breakfast. Continue your tour visiting the Library of Alexandria (from outside) and the Fort of Quitbay (from outside).
Day 05
¯ Visit to Coptic Cairo;
The Hanging Church, Church of St. George and Church of St. Sergius.
Afterwards visit to Khan El-Khalili Bazaar.
Day 06
Free time shopping at City Stars Mall.
final departure according to your flight details.

this is a template program for cairo and alexandria and you can also visit for an overday so you can back to cairo at the same day or fly from Alexandria airport.

Why not Luxor?

I could not imagine a trip to Egypt without seeing the Valley of the Kings, Temple of Karnak, etc.

If at all possible, try to get there, even if you have to skip Alexandria.