If you only have a weekend and have to stay in Nairobi, go to:
1. Nairobi National Park (Assuming you're not going on another safari to one of the much better parks)
2. Giraffe Center.
3. Elephant orphanage. (Make sure do go to David S.'s orphanage.)
4. Nairobi Museum. (Especially if you like history, culture, anthropology)
5. The Carnivore, if you like meat.