As a result, I chose to book a separate tour for the first day, along the same lines as our trip to Southern Peru. My guide and driver from "Casual Cairo Detours" would cover many of the critical sights in Cairo that weren't included in my On the Go Tour.
Actually, when I first arrived into Cairo, the tour company informed me that they did have some "optional tours" available: the famous Egyptian Museum, the Cairo Citadel, Coptic sites, or a sound and light show. But, since I didn't know about this beforehand and I had already booked my "Casual Cairo Detours" tour, oh well.