You will be surprised about Cairo. Egypt is not a fully muslim country but a country with a mixed population especially in Cairo. And for sure not all Muslim women appear in what we would consider muslin costumes. An evening outing in Cairo clubs is very similar to any big mediteranean city.

If you want to stay at the airport, there is a nice Moevenpick hotel in five minutes driving distance and they pick you up for free and take care of all formalities. Last time I was there I had a day rate of about 60 Dollars, nothing to talk about.

If you do not use a "Meet and Greet service" (what I always do) you have to buy a visa stamp before going to the immigration officer. These are sold by the money exchangers on the left side of the hall where immigration takes place.

I am a little bit reluctant to take taxis from the airport late. Not because they are expensive or I am afraid to get robbed. No concerns about this. The only frightening thing can be the car itsself - you won't see these on the roads in the US or Europe. No problem during daytime or in heavy traffic, they have no chance to drive fast. But I do not like these guys driving full speed on the empty road into town at night with something that has seen better days and could be described as a car 20 years back in the past.