Spend a day around the Pyramids. Have breakfast at Khufu's, visit the Grand Egyptian Museum, and take a camel ride at the Great Pyramids of Giza
Take a tour around Islamic Cairo: visit Al Moez Street, Khan El Khalili, Cairo Citadel & Sultan Hassan, and the Mosque of Ibn Tulun
Visit the Coptic Cairo neighbourhood. See The Hanging Church, famous for being built over the gatehouse of the Babylon Fortress, making it appear suspended in the air.
Spend a day or two in the North Coast (where the wedding ceremony is). You'll find pristine beaches, nice restaurants, and maybe a few parties during the long weekend. I've shared a few good hotel options, but Airbnb could also be feasible if you're a larger group.