Quiz a local on what the most unique structures in town are and they'll probably mention Cairo Tower. It's one of the first things that'll catch your eye when you start exploring.
When it comes to things to see and do in Gezira, Cairo Tower is recommended by fellow travelers. And in good news for your budget, entry is free. Egyptian Museum, Khan el-Khalili and The Hanging Church will round out your day and are not far from the modern piece of architecture.