However there are two museums that I strongly recommend anyone visiting Cairo make time to see.
Coptic Museum. Image from Wikipedia.
The Coptic Museum in Old Cairo was renovated in 2005-06, and has the largest collection of Egyptian Christian artifacts in the world, all of it helpfully labeled and signed. It is the highlight of Old Cairo, of which Coptic Cairo is a major part. While you are in Old Cairo you can also visit a number of working Coptic churches, and the Ben Ezra Synagogue.
Old Cairo is easily reached by Cairo Metro Line 1 to Mar Girgis station. The Museum entrance is directly across from the Metro exit, while Coptic Cairo can be accessed by a pedestrian underpass under the city wall, off to the left and across the street as you exit the station.
quezz notes that this neighborhood is under threat, so it's best to see it while you can.
Museum of Islamic Art. Image from Wikipedia.
The Museum of Islamic Art is one of the greatest Islamic art museums in the world. It reopened in 2010 after an eight-year, multi-million dollar renovation. The items displayed are placed in their historical and thematic context, well-labeled with explanatory signage in Arabic, English, and French.
The museum is about a fifteen minute walk from Naguib station on Line 2.
Both museums were largely empty of tourists when we visited on a weekday. Most of the other visitors in the museums were local art students who sat on the floors and benches sketching pieces.
One of the other visitors we met was an Egyptian expatriate, now living in Paris, who had come back to Cairo many times over the eight years of the Museum of Islamic Art's long-delayed renovation and been disappointed to find the museum still closed. He expressed his joy at being able to visit the museum where he had done his dissertation research many years before. It was complete chaos back then, he said, but it was beautiful now.
He was absolutely right. The Egyptian Museum could use a makeover like the ones these two museums have gotten.
Both museums are world-class, and both offer a cool respite from hot days in Cairo. Neither has a working gift shop or a working cafe, however. And neither allows cameras.
The Coptic Museum's website: http://www.coptic-cairo.com/museum/about/about.html (Note that the ticket prices have not been updated.)
The Museum of Islamic Art's website (www.islamicmuseum.gov.eg) appears to be down at the moment, but the BBC has a gallery of photos of the museum and some of the pieces in its collection.