As many people agree, this is one of the most beautiful mosques in Cairo.
It's also the oldest intact mosque in Egypt (the oldest mosque, the Amr Mosque near Coptic Cairo, is too heavily modified to be considered original), and preserves its 9th-century Abbasid style (the Abbasids were the great classical Islamic dynasty who ruled from Baghdad for centuries). This also makes it very different from other mosques in Cairo; there is no grand entrance, but rather two concentric walls and a huge courtyard framed by elegant arcades. Make sure to explore and see the remains of stucco decoration on the arches on far (western) side from where you came in.
You'll be asked to leave your shoes or wear special covers over them. The caretaker will ask for money; be reasonable and give only what you feel is adequate, as there is no official ticket (10 pounds is already plenty for an informal visit to most mosques, including looking after your shoes). He may ask more for the minaret, but, as far as I can tell, access to the minaret is unrestricted and therefore shouldn't really count for more baksheesh.