The ultimate climbing desire of the outdoor climber in Kenya is to summit the snow-capped Mount Kenya.  The highest peak, Batian ,  and second highest,  Nelion, require technical climbing class 5.1. So most climbers are satisfied summiting point Lenana that does not require anything more than a good pair of boots and socks.

But there are other climbing opportunities in such as
Aberdare
Cherangani
Kyulu
Masaai land
Mathews ranges
Menengai
Longonot
Suswa
Kamba land
Marsabit
Elgon

For the technical climber, it is prudent to liaise with the Mountain Club of Kenya,  wmck.or.ke.  They are a good source of information and contacts.  Their offices are at the Nairobi Sailing and Sub Aqua Club, adjacent to Langata Shopping Centre. They hold club meetings on the second and last Tuesdays of each month.

But for simple hikes that do not require technical gear, many tour companies in Kenya will get there. Facebook is a good place to seek them out and review the member comments