The vendors in Alexandria were especially aggressive right outside the cruise port. We had already experienced the vendors at Giza so we knew how to just keep walking, don't talk but one guy stuck to us like gum on our shoe and wouldn't leave us alone until we had to tell him "Leave us alone". We had a little boy follow us and try to get into my friend Terry's back pack while we were walking!
Once we were about 6 blocks from the port we were fine.
I never felt unsafe, just bothered but do watch your bags, purses etc and I can't emphasize this enough especially for women, please cover up as the local women do or expect to get comments.
Be careful, in the Abu Qir area, of drifting by error into the military zones...easier than you think. I did it, trying to find the beach (which turned out to be mined anyway). The result was an arrest by any other name by the military (after I was found near a rocket battery...) and a day of generally polite interrogation by the Mukhabarat (secret police) in one of their villas and then at their HQ. I was pretty glad to be released eventually late at night. Be warned. A good idea, if you are likely to be in the city for more than a couple of weeks, is to register your presence with your consul. There is a British Consulate in Alex (in Rushdie) and most other major powers have a consular presence, mostly in that same neighbourhood.