For serious bargains the places to go are the City Market in Nairobi and any little kiosk (shop) on the side of the road. A stop at the Equator is a must. Shopping in Kenya can be a lot of fun and a large pain at the same time. The first thing to realize is that bargaining is a must. Almost anywhere you go to buy something you will be able and expected to bargain.
Try African Heritage in Nairobi as well as Utamaduni in Langata (ten minute drive outside of Nairobi). Merchandise there is more expensive but the selection is greater. Paying by credit card is another advantage as well as having the larger items shipped home.. If you are looking for other African wares in Nairobi, here is a list of shops that I like and/or trust. These places are also exceptions to the bargaining rule.
Excellent quality suede clothing, some beaded by local craftsmen, is designed and made here. It is popular in the local area as well as sold as overseas. Stop by and see for yourself. Tell them Bwana Zulia sent you, you might get a "cupa."
Mostly fabric shops, but there are also some small "dukas" that sell Khangas (printed fabric) and Kikois (woven) those ubiquitous pieces of locally made cloth that everyone wraps around themselves at one time or another. They make great gifts, won't break your budgets and there are many different colors to choose from. Walk up and down the street for a few minutes to get the overall picture and then make your move. Prices there are about as low as they get, certainly lower than most shops in hotels and other heavily trafficked tourist areas. A little bargaining is allowed here, but it is tough adn usually reserved for bulk rates.
(Karen shopping center) is a horse lovers paradise with a ton of horsy gear. but there is also a selection of some rather unique items from all over Kenya. Hand blown candlesticks, canvas bags and safari chairs, wrought iron chandeliers. Check out the rest of Karen while your there, the chemists is a hoot and the Karen Provision Stores could have been dropped right out of the wild, wild west.
This is a bigger, if not necessarily better, African Heritage. It is absolutely huge with tons of things to buy. Again, you will not be getting the best price for the Kenya stuff but you will at least be getting good quality. It can also be a "idea" place to start you off on your trip.