Kiddo,
We went to Egypt twice and would definitely go back again, even to the same places. Couldn't recommend a place more to do what you are planning.
There's loads of details which I put on (look under Egypt Misc, do a search for "Ali Baba Hotel - Hurghada, & Cairo, & Luxor", John & Brenda)
We booked through Amsterdam with a Dutch company, it was a bit cheaper at the time, but you need the bit of Dutch to get through the website... you could get a flight with Transavia, but they are VERY cramped seats.
Cairo is a culture shock , and there are plenty of chancers about the airport. Know what you should be paying for taxis etc., or arrange the hotel to pick you up. When you are getting currency, request the smallest denominations that you can. 20 euro is an absolute fortune over there, it can be hard to taxis to break the equivalent egyptian note (but they all accept euros / dollars / STG). 5 euro note is very handy to have as a "get you home" backup if you run out of cash.
We didn't like Cairo at all, and stayed only a day and a half. I'd say the other places are better. If you're flying into Cairo, I'd recommend doing the Pyramids and museum, spending a night and getting down to Luxor on the night train the next night, this can also bring you to Aswan, and the Abu Simbel temple, which is meant to be out of this world. Having seen some of the "lesser" temples in Luxor, I am really sorry we didn't get to Aswan and Abu Simbel. The guide books say to fly in and out of the area in the one day, as its pretty desolate and you're also heading for the Southern border country, which = bandit country, anything goes really.
Hurghada was really relaxing, but not much to see in the way of land-based sights. However, under the water, there is much more to see and do... if you haven't dived before, and can swim well, try and do a PADI open water course (international certification so you can use it again, takes 4 days, 300-400 euro including 2/3 boat trips), it really is well worth the money. If by any chance the dive organisers bring down a video cam with them, buy the video, it is one of the best souvenirs we have from Sharm El Sheikh (where we went Summer 2004). If you're diving and flying, you have to leave 24 hours between diving and then flying, same applies to St. Catherine's monastery in Sinai, due to the altitude.
Sharm El Sheikh is similar to Hurghada as its a big dive spot, not so many natural or historical attractions, its more of a European resort style place, a bit more expensive than down South. We went back there for a relaxing week in a hotel, of which we spend 3 days diving. The seas were rougher there, so it was more challenging, not as much fun as in Hurghada.
DOs:
- go diving, its really worth it (cheaper than getting certification at home also)!
- spend a bit on the hotels, its generally cheaper than in Ireland
- move around between different centres, there's so much to see and do there
- talk to the locals, they have an almost Irish nature to them!
- try and go in May or Sep, hot, but not too hot! If you go in June, July August, I'd recommend sticking to the coastal spots
- buy a lonely planet, it was invaluable for us ...
Don't
- get a hotel without air-con
- plan to spend long in Luxor during July / Aug, its 40 degrees.
- hire a car (cities are crazy, and they drive without headlights at night, they flick them on if they spot something on the road - seriously, you'd have to see it to believe it!)
- try to do too much, it will take from it all if you do, you can always go back for a 2nd honeymoon!
- eat any uncooked food (e.g. lettuce washed in local water gave us some dodgy rumblings for the first few days)
- forget that arabic goes from right to left, we spend ages looking at the 107 bus, wondering when the 701 would arrive to take us from the airport into town...
If you have 3 weeks, you could do the following:
arrive Cairo,
Night 1 in hotel, see the museums and pyramids,
Night 2 in hotel, check out whatever we missed in Cairo,
Night 3 travel to Luxor on train
Straight off the night train, dump stuff in hotel, get on a tour to the valleys in Luxor (the coaches are all gone by 8am, due to the heat during the day)
Night 4 Luxor, do the temples around Luxor
Night 5 Luxor, get back on train, go to Aswan, see dam and Abu Simbel
Night 6 & 7 : felucca / cruise back up (down the river) to Luxor
Night 8 Luxor, get to Hurghada (we had to public bus it when we did this, I'd recommend a flight or tour bus, it was kind of dodgy)
Night 9-15 stay in Hurghada, rest, get a tan, and dive
Night 16-18 Sharm El Sheikh, do St. Catherine's Monastery and Sinai (early start I think). Sharm itself has a pretty good nightlife, but its all centred on beach, hotels and diving as far as we could tell (not that we ventured far though!)
If you're not into the beach or diving, you might want to cut down the time in Hurghada, spend it in Cairo or Luxor instead. Luxor is very hot in mid-Summer though... it restricts what sights you can visit during the daytime. We didn't really fancy the Nile cruises, as it was similar to the Liffey, and there were a good few mosquitos where we were... but the cruises are very popular, I wouldn't put down what I don't know...
You might also consider heading for the desert oases or into the delta region up North (Alexandria) - I didn't look into this due to our time constraints, but it might suit you.