My best friend and traveled to Kenya and Tanzania in January 2002. Before she arrived in Nairobi, I was on my own for 3 days. I walked around the city centre and around a couple of other neighbourhoods - approx. 10 blocks away from my hostel. I never felt I was in danger. No one ever came up to me to ask for things. The people at the hostel said I wasn't approached because I wasn't wearing any gold/silver jewellry - a dead giveaway for an outsider. They also said I looked like I belonged there because I was wearing a skirt...now it was only a plain brown nylon skirt (with Birkenstocks) but the hostel staff said that wearing long skirts is very 'African'. I did not wear hiking boots and quick dry pants....also a dead giveaway.
Further to what you're wearing on your person, I would say that you have enough common sense not to go into areas that tourists don't go. That you don't wave around your money. That you don't walk down dark streets at night.
People think that Nairobi is extremely dangerous and I'm not saying that it's not BUT may I also put forth that LA and Chicago are extremely dangerous as well...
My friend and I had an amazing experience everywhere we went and more importantly, we met amazing people.
It was the best trip of my life so far. I hope you have the same experience.