John Billman Saqqara is a not to be missed day trip from Cairo and would be very high on my list.
Also Dashur, Meidum, Memphis, Abusir, etc. you've really got the pyramid age of the Old Kingdom at your fingertips.
More unusal day trips could include Tanis, Tell Basta, Alexandria (by train), etc.
Finally a hidden gem of Cairo is the little visited Agricultural museum, it has a large and worthwhile Ancient Egypt gallery and very friendly and helpful staff.