Kenyan food is not so much variegated: the national dish, and you will find it everywhere, is the nyama choma, that is grilled meat (beef, chicken, turkey, mutton) dressed with salt. As a side dish, the ugali (white porridge, used instead of the bread), the sukumawiki (spicy spinach), French fries.
For breakfast, either tea or coffee with mandazi (lightly sweet fritters). Moreover the fruit is very tasty and various everywhere: pineapple, mango, papaya, oranges, passion fruit, and many others.
In Lake Naivasha area you can taste the lake fish, and on the coast any recipe with fish, dressed with spices as from a strong Indian influence. Moreover along the coastal area you can taste delightful fruit milkshakes.
In Mt Kenya region many dishes are based on black beans.
In Nairobi many restaurants propose food from all over the world; particularly worthy are the Ethiopians (where you can taste the zighini: a sort of thick crepe is the base for a mix of different meat, vegetables and eggs, usually very spicy); again in Nairobi some restaurants are specialised for grilled meat: once they used to serve even wild animals as giraffe, crocodile, wild beast, dromedary, etc, now only meat from breeding animals: at the Carnivore the fillets are cut from a big spit, carried by the waiter up to when you ask him to stop.. It's not the paradise for vegetarians, as for the great majority of traditional Kenyan food!
As for drinks, beside water (pls always check the bottle to be closed and with an unbroken plastic protecting the tap: for those who are not used to this kind of water an imprudence may mean an inconvenience all travel long), you can drink soda (generics for all sparkling drinks) or beer (the most popular local brand is the Tasker, even Malt). Almost everywhere you can even find superalcoholics, but be careful because some of them, mainly found in the poor areas or in the slums, are illegal and may be very harmful for the health, and even be lethal.
Finally, a special mention for the chai (tea), often prepared with milk and ginger.