Kenya offers everything, from Mountain climbing, desert safari, wildlife safari, beach, etc. I have traveled to Kenya more than 3 times, but the best time to travel is March and April since it is normally low season.
Kenya is really amazing, I have been there 4 times and each time I felt like a first time, you can't really exhaust all the attractions in Kenya, but at least in 3 weeks you can be assured to enjoy your vacation.
If you do decide to visit Kenya, Masai Mara, Lake Nakuru, Lake Naivsaha, and Mombasa should be top on your list, that is, if you have the money, it can be realyy expensive so you need to plan your safari very well.
I have lived in Kenya when I was young, around Mount Kenya area, the place is amazing, you should consider adding it in your itinerary especially Laikipia where there are a few private parks, and also Nanyuki and Aberdares.