If you want a great dining experience...go to "Carnivores" just outside the city. Its a short cab ride and well worth it. They cook every imaginable meat and serve some incredible sauces to go along. In addition to beef, they offer wildebeest, giraffe, crocodile, gnu, etc. Its an incredible atmosphere with these Kenyan dudes walking around with freshly cooked stuff on skewers which they then lop off onto your plate. Awesome stuff. Also, the bar is jumpin' with a lot of Euro folks and great music. Its outside and adjacent to the restaurant.
The hotels in Nairobi are very nice and have pretty decent security. The threat lies in the ride from the airport to the nice hotel area and the downtown vicinity immediately adjacent to the hotels. In my experience, I felt very safe in the hotels and doing the cab thing. Walking around, especially at night, was not a good idea.