On February 14, I returned from three weeks in Nairobi and Kenya. I was part of an organized group, not alone. However, on Saturday, Feb. 3, we were on the same stretch of road on the same day as the two American women were carjacked and killed. (Ironically, when I arrived home in Phoenix, I turned on the TV and the first thing that I saw was a news report of a violent carjacking in Phoenix.) (Also, the area around Kinoo is known to be risky. For some reason, the women had stopped in their car. When approached by the gunmen, they expressed some resistance. All of these things are things not to do.)
I have visited a number of other large cities around the world. Nairobi is more complex and chaotic than some; less complex and chaotic than others. Most Kenyans are delightful, optimistic, open and very trustworthy people. However, there is indeed danger and violence in Nairobi (as in most other major cities). All reliable hotels have extensive security and you have a good measure of safety within their grounds. However, even Nairobi residents are aware that after dark, things become less secure.
I do not think that a woman by herself can go out and about everywhere in Nairobi. Beginning with the airport, you will be confronted by masses of people and vehicles and likely accosted by hustlers trying to sell you whatever they think you might want or need. They will try to insist on helping you with your luggage and even grab the luggage cart right out of your hand.
Under your circumstances, the best advice is to contact the hotel where you will be staying and through them, engage a reliable driver and vehicle to meet you at baggage and then drive you around Nairobi the next day for sightseeing.