Having worked in Kenya the last two summers, my impression of Nairobi itself isn't so great. There are plenty of attractions just outside the city as others have mentioned - the game park and Karen are solid options. The Olorgesailie pre-historic site and museum are about a 3 hour drive away towards Lake Magadi if you're interested in that sort of thing. The drive itself is quite nice since you descend into the arid Acacia scrubland of the Rift Valley very suddenly after driving through the highlands; some really great views of the Rift along the way. There are local guides who staff the museum but you could just wander around the few exhibits yourself and then do a self-guide tour of the old excavations that have been preserved for tourists. Just be sure to bring lunch and lots of water since there is nowhere to stop nearby.

If you're stuck in the city of Nairobi itself, you can buy some touristy stuff and gifts at the Masaai market when it occurs once a week. The permanent city market charges more and will hassle tourists more aggressively but you can get some nice stuff there if you stand your ground on prices. The real exception to the drabness of Nairobi is the food. Great Indian, Ethiopian and Italian food are available. For Ethiopian I would go to Habesha; tasty and fairly cheap little place near the intersection of Uhuru Highway and Mokhtar Dada St, ask at your hotel for directions. For Indian Ocean cuisine go to Tamarind - it's expensive and delicious and everything there except the raw oysters is worth eating. For Italian there are a couple of options - Trattoria is good but the service takes forever. Good for large parties who want a 3 hour dinner to drink and talk over. The best Italian option is http://www.mediterraneorestaurant.co.ke/ This place is outstanding; pricey but completely worth it.