First of all, you'll likely want to go back to the Egyptian Museum, as one could spend a week there and your tour will likely only give you a couple of hours. From there you can walk around the city a bit, there are a few nice squares with parks and interesting cafes and stuff. It sort of depends on where you're staying and what you're interested in.

A definite must is the Khan al Khalili, the traditional "souk" at the heart of Islamic Cairo. Go during the day and just be firm about saying no if you don't want to buy anything. But definitely do go into a perfume shop. They sell really nice glass perfume bottles and you can buy 10 in a box for not much money (makes great gifts.) I'd also recommend crossing the street (via the underground walkway) and taking a tour of the Al Azhar mosque. It's quite stunning.

Khan al Khalili is about a 10 minute taxi ride from the museum. If you have a good map and someone to go with (I probably wouldn't do this walk alone, though, really, you'd be perfectly safe), the Al-Suhaymi house on the edge of the market is very cool, too.

Where are you staying? You don't mention the Giza pyramids, but surely they're already on your itinerary, right? Another possible half-day outing is what's known as "Old Cairo" -- south of the main part of the city, which is where all the old Coptic churches and the old synagogue are.

As the previous poster said, Cairo is a large bustling city. You'll stick out as a Westerner, but assuming you're dressed appropriately (which we already covered in the chicks thread, ) you'll be fine.