The Nairobi National Park gives the opportunity to see a part of the Kenyan wildlife not too far away from Nairobi. They are running free in the park, you might be lucky and see the big 5 Lion, Leopard, Hypo, Rhino, Elephant (although there are no Elephants in the Nairobi area), but it all depends on time, luck and your ability to see them.
For sure it's worth a visit but I heard from my guide that the best time is in August as it's the middle of the migration and the National Park is full of animals and wildlife. It's a 42 Square Miles park that is about 15 min drive from Nairobi's center, it also has the Burning site where President Moi Burned all the Ivory and Skins that were gathered by the police in an effort to stop the unnecessary killings of Wild Animals.
I was lucky enough to see some Lions in the shade, Giraffes, Monkeys, Zebras, Gazelles, Rhino (very far away) and Ostriches; it was definitely a good trip.