I am so excited for you!!! I went to Egypt a couple of years ago, just Cairo and around. Unfortunately we didn't make it to Alexandria.
I think most of what I'd say has been covered. You could wear a wedding ring (or just a wedding-ish ring on that finger) and be prepared to lie about a husband or fiancee if asked. I don't usually advocate lying but in that respect it might be advisable. I was with a group of friends including men which helped a lot - I would have expected more harassment otherwise from all I've heard. Definitely wear long skirts (which I found very comfortable in 40 degree heat) or baggy (prefereably linen) trousers and tops that at least cover your shoulders, preferably elbow-length sleeves or so. Also the tip about a drapy scarf/shawl is good as you can use it for covering a low-cut top, putting on your head for heat or modesty, etc.
Although it probably makes me sound prejudiced, I'm extremely wary of Arab men partly from travelling in North Africa and partly from experiences living in Europe (more the latter, really.) The tips already have been good. Avoid eye contact and smiling at random men. I doubt you're the type to get swept away by extravagant compliments (and believe me, you will get at least some extravagant compliments) but, you know, if that cute guy wants you to marry him and run away, I'd say don't. Incidentally, it is a documented fact that Egyptian men (in particular) don't only harass western women because of the slutty image, which is a problem generally in that part of the world. They also harass and assault their own women pretty routinely. Again, I know this makes me sound biased but it is a well documented fact.
In Cairo, of course you have to visit the Giza Pyramids but Saqqara (with the older, smaller pyramids) is amazing too. Less touristy as well, though I hear that tourism is way down since the revolution so the Giza Pyramids might be relatively quiet. Also the Egyptian Museum, and the Citadel. The City of the Dead is kind of a trip - though I felt a bit intrusive as it is where relatively poor people live among the tombs, just a neighbourhood really. But when I walked through there with my friend, people were greeting us, wanted to know where we were from and seemed really happy we'd walked through! And you MUST go to Al-Azhar Park if you have time, it was a magical escape from the crazy city.
At the Giza Pyramids, if someone tells you that you can't walk up to the pyramids on your own any more, and you must do it on a tour, and their tour is the best, it's a load of crap. (And someone or several people will probably try that.) Just ignore them and walk away - unless you really want to do a tour (with horse drawn carriages, etc) and it seems good. I paid to go into one of the pyramids - Khufu, I think, not Cheops. The slightly smaller one. It was pretty cool though there isn't loads to see.
Stay in groups. I wouldn't go off alone though you'd probably be ok, but better not, I'd say. If you're with just one other person at some point, it might be better if it's a man, although people will likely assume it's your husband and will ignore you and talk to him only (in a lot of cases.) Although, in Morocco I was with just one female friend and basically we were fine. We got some hassle and marriage proposals but generally it didn't feel threatening. I've heard it can be a lot more threatening in Egypt though my experiences weren't bad, but again, I was travelling with men.
Accept hospitality if it seems wise, perhaps in a large enough mixed group. It's a very hospitable culture. Tell people you're happy to be in their country and enjoying it, they appreciate that.
Keep an eye on the security situation as obviously Egypt has been unstable the last 2 years. (I was there six months before the revolution.)
Cairo is insane but a total trip. I was on a natural high a lot of the time there. I think on my own I would have found it scary but it was fun with other people. I've also been to Marrakesh (Morocco) and that is much smaller but felt crazy, too, with all the traffic and crowds. So I imagine Alexandria will feel kinda nutty as well. Be careful of the traffic, but eventually you do just have to run out into the road. The best is if you can attach yourself to a group of locals to do it. The cars will weave around you if you're relatively sensible. You'll get used to staring death in the eye when taking cab rides and the like.
I don't think Egyptian food is amazing (I liked Moroccan much more) but just try different things and have fun. It's cheap. We ate at a great restaurant in Cairo (more of an ex-pat restaurant with European-North African fusion food) which was still pretty cheap for us, and cheaper places really didn't cost much. The water is bad (at least in Cairo and probably elsewhere) so drink only bottled water. You might even want to brush your teeth with bottled water. It's also better to eat cooked veg instead of something washed in water that could make you sick.
Also, try not to laugh directly in the guy's face if he goes "Hey Beautiful! You walk like an Egyptian tonight!" (It wasn't directed at me but I overheard this in the bazaar, a guy trying to get a western girl's attention. Hilarious!) You'll definitely get called princess, gazelle, pretty lady, etc etc... Hey ho!