This is not Cairo's easiest site to find, partly because it's known by several different names. It is worth the effort, though, if you like tiles. The mosque takes the "Blue" name for a wall of multicolored Turkish tiles that was installed during a mid-17th-century renovation by an Ottoman officer, who brought in the decoration from Istanbul and Damascus. The mosque is also known by the officer's name -- Ibrahim Agha Mustahfizan. The formal name of the place, however, is Mosque of Aqsunqur, who was the original builder back in 1346.
There are three tombs in the Blue Mosque, one each for Aqsunqur, Mustahfizan, and Aqsunqur's brother-in-law, who sat on the throne 5 months after his 6th birthday before being killed by his brothers.
Apart from the tiles, the biggest reason to visit the mosque is the minaret. The 80-plus-step climb is a little scary -- the steep swirl of a staircase isn't in the best of shape, and the lights are pretty bad -- but the view from the top over the old town all the way up to The Citadel is fantastic. I also enjoy the fact that it really is tucked into a part of the city that few tourists venture into. This is not a tour-bus accessible area, and you can easily be the only person standing in the modest central courtyard.
Starting on the northwest side of The Citadel, walk north on Sharia Bab al Wazir (which runs away from the base of The Citadel) past the first major intersection and another five streets to the right (big and small) before the mosque appears on your right. It takes me about 10 minutes to walk.