A good friend lives in Alex and was asked for recommendations for hotels. Her post was so useful I asked her permission to quote it.
Regarding hotels. The three big ones in the centre are the three old ones. The Sofitel Cecil, and then the Windsor palace and The Metropole all are on the corniche with sea views.
Everything else in that area is a distinct 3* max and its a case of take your chances.
All other hotels are then spread out along the length of the corniche. In order of distance from centre: the Royal Tulip hotel, Mediterranean Azur, the Plaza (lower 4* similar to Emilio but expensive prices), Four Seasons, Mercure, Hilton corniche and then right at the end of Alex which is an hours drive from the centre is a cluster of Sheraton, Aifu horizon, and Helnan Palestine.
The three in the centre have no beach or pool.
Of the others all have either a beach access or pool except for the mercure and the plaza.
Any of the other hotels would take between 25 mins and an hour to get to the city centre depending on how far out.