Be extra careful crossing the roads in and around Tahrir Square. Egyptian motorists drive fast and seldom obey red lights.
That said, Tahrir Square is arguably one of the safest areas in which to stay and visit, being full of heavily-guarded government offices, the American University of Cairo, international hotels and cultural institutions some may argue, of course, that this makes the area more of a target for terrorism and unrest. Also, Tahrir Square is a frequent gathering spot to stage political protests, which sometimes can become violent and are best avoided.
Be careful at Midan Tahrir, or nearby Midan Ataba, as these seem to be epicentres for the touts and "helpful locals". They will innocently ask you where you where you are from and then point you in the wrong direction in direct you towards a friend's business. Only at the pyramids does this happen more often.