It seems that Tahrir Square is the focus of any protests in Cairo. That's where the 18 day democracy movement was based. Just a day ago out-of-work Egyptian police held their own protest in the square (they haven't been paid since the crisis).
There are a couple of big name international hotels close to the square, one of them at the end of 6th October bridge, the scene of some of the deadliest clashes.
I won't name them, because although the situation remains unstable, there hasn't been any significant violence in the last few days. Similarly, haven't heard any more reports of vigilante groups and local protection forces taking unilateral action.
However, UK, US and Aust authorities are still recommending you should rethink plans to visit Cairo for the time being. almost 10 years ago
UK prime minister has visited Down Town Cairo yesterday February 22nd where it witnessed the revolution and he was walking freely from Ramsis street till Tahrir square and greeting people in the streets.
Cairo is now becoming more safe in most parts if you would like recommendations of quiet districts you might consider Pyramids area, Maadi and Zamalek. That is not to say that Down Town (Tahrir area) is not safe but still you might find protestors raising their demands. almost 10 years ago