A couple more places to add. Saladin's Citadel is well worth the trip, it sits quite high up and gives views above the city even over to the pyramids. There is also the famous market area, can't remember the name but the hotel will know, it's nice with plenty of stalls and street cafes.
On avoiding the tourist traps, some good tips above. On taxis, white taxis are good but black ones are everywhere and so you will have to take them at some point. They clearly try to rip you off and they rely on the fact that Westerners don't really know how to haggle (Arabs make a sport of it). There are no hard and fast rules, but I would always keep in mind that even if you think you're getting ripped off it's still going to be cheap by major Western city standards so don't waste too much time on it. My other concern for you would be having a family of 5, most taxis are 30-year old imports from Eastern Europe and fitting 3 in a car is difficult! Be very careful too, don't ever leave just females in a taxi on their own. If your hotel offers bus tours, consider these even if more expensive as the hassle-factor is so much lower.
Dealing with beggars is fine, they may give you the odd "f*** you" but you can thank American television exports for their few words of English, don't take it personally. The bigger issue is the "unofficial tour guides" who will latch on to you at any given opportunity. These tend to be twenty something males with good English and start friendly with some advice on the sights (as above, little information is actually provided at many tourist areas), but in the end it tends to be a hard sell often to take you away in a car or horse drawn carriage somewhere. My advice is to say politely "no thanks, I've been here many times" when they approach. They'll likely still follow you and talk to you, just be firm but nice in saying no thanks. If you really can't get rid of them, keep a look out for any tourist officials or police/ security (they're few and far between) as they'll get rid of them, or simply be prepared just to give them a small amount of money just to go away (e.g. $2 or $3).
Overall, Cairo is a fascinating and vibrant city and well worth the visit. Don't be put off by any of the negative comments above, it's all part of its charm. For example, though haggling for everything can be annoying to many Westerners, actually it can be good fun if you get in to it (e.g. at markets). The elaborate façade of arm gestures, head shaking, walking away, coming back, being their friend, being their enemy, drinking coffee with them and then, only once all the above is complete, coming to a price is great fun and will stand you in good stead the next time you take your car to be repaired!