Due to the altitude and distance from the base to the peak, it is NOT possible or safe to attempt to reach the top in one day. Additionally, the Kenyan government also requires you to have a guide to reach the summit.
The three most popular routes up Mount Kenya start from Sirimon Gate to the northwest of the peak, Naro Moru Gate to the west, and Chogoria Gate to the southeast.
Going the Sirimon route is the best choice. It lasts 4 to 5 hours and is around 13 km. The price is 50 dollars per person.
The easiest way to get from Nairobi to Nanyuki would be via a local matatu. The trip takes 3 to 4 hours.