Going around:
A cruise in your car around Zamalek would probably not seem like the best thing to do that is a result of the traffic laws strongly applied in Zamalek as well as the traffic itself.
There are no parking spaces anywhere and most streets are one way leaving the problem of figuring out which ones to the drivers.
A walk in Zamalek would probably be delightful keeping in mind that it is not that big after all.
In this walk you can come across many interesting sites let alone the greenery around the south.
One can see the famous lion statues decorating the old "Qasr El nil" bridge as well as the statue erected in memory of the great Egyptian leader "Saad Zaghloul" on the end of the same bridge.
Another piece of art to be witnessed is the "Abu El Ela" bridge designed by American engineer William Scherzer (not by Alexander-Gustave Eiffel like the strong rumor states).
One can also can gaze up to the Gezira tower or take a stroll in the opera gardens but entering these facilities and making use of their utilities would also be a nice idea.