Let me give this a stab...

First off, how old is your daughter? The Egypt Museum in Tahrir Square is a must see, if only for the Tut treasures...but even a small child might get bored. If your time is limited, you can hit the highlights in under 2 hours.

Obviously the Pyramids. But don't rush them like most tourists do. Walk around them. Go inside, is possible. Get to know them. Take an overpriced horse/camel ride around the site. Gaze at the Sphinx. Spend hours (again, if your daughter is young, not so much...). They are truly amazing and nothing can prepare you for how immense they are. When you're done, have lunch/a drink at the Oberoi Mena House hotel, a stone's throw from the entrance. Seriously, don't rush this.

About Luxor: As amazing as it is, I'd save it for another trip; you just won't have the time, and there's plenty to see and do in Cairo. Let me know when you're going, and I'll give you the scoop (I've been there over a dozen times...).

Islamic Cairo is fantastic, near the Hussein/Al Azhar/Khan al Khalili area. Don't get ripped off in the market, but do browse and poke around. The mosques in this area are hundreds of years old and still used as places of worship and education. (But make sure your shoulders/knees are covered...no shorts here, or anywhere in Cairo, really.) Have tea (and a waterpipe?) at Fishawi's in the Khan. It's been open 24/7 for hundreds of years, and while touristy, is a serious local haunt too. If you want non-street food, try Naguib Mahfouz's cafe, in the heart of the Khan.

You really must do a felucca (sailboat) ride on the Nile, one of the most sublime experiences at sunset. Just remember: (a) don't touch the water, (b) bargain bargain bargain, then bargain some more, (c) don't get bullied into paying more than you agreed to, and (d) make sure to be explicit about how much time you get and where you go. But certainly do it!

If I were you:

Day 1: wake up late, go to Islamic Cairo and the Khan, shop, bargain, visit Al Azhar, have lunch at Naguib Mahfouz (or try the fateer joints near the entrance to the Khan)...afternoon to relax in a cafe or your hotel, then felucca ride/walking around town at night

Day 2: now that you're rested, hit the Pyramids as early as possible, before the busses arrive...then relax over lunch while the hordes descend, returning when they leave. Be sure not to miss the solar boat museum on the far side of the biggest pyramid...the oldest intact boad in existence, over 5,000 years old...super neat! Late afternoon to relax (you'll need serious down time in Cairo), before dinner...maybe on a floating restaurant? A trendy Lebanese place (I can recommend)? If your daughter is young, you might want to hit Felfela's Village on the way back from the Pyramids, kind of a Middle Eastern Chuck E. Cheese.

Day 3: Egypt Museum, more walking, maybe Sufi dancing (only on Wednesday)? Could also check out "Old Cairo" with its Synagogue and "Hanging Church." Or maybe the City of the Dead, with its tombs and mausoleums? Another terrific Islamic Cairo stop is the Gayer Anderson House (a James Bond film was filmed there) and nearby Ibn Toloun mosque with its unique external spiral staircase minaret.

Hope this helps... Feel free to reply with other quesitons.