Camping can be done anywhere in Kenya but the camping sites are not that many. This therefore means that you do your homework well. There are private and public campsites.

Private campsites include luxurious camps where you will find proper facilities for your comfort. They also have flush toilets and hot showers with the provision of firewood for your warmth at night basically, you will be outdoors but comfortable.
The public or park campsites only provide the basic requirements which are water and shelter. It is advisable to bring your drinking water. Sometimes you have to bring your beddings too.
To be sure, you need to ask whether mosquito nets will be provided. Remember Kenya is a tropical country and mosquitoes love camping too. Camping in Kenya is a fun way to experience adventure and this is especially when some of the wild animals start grazing around your campsite without a care in the world.
At night, a big campfire is lit and you can sing songs and dance to traditional Kenyan songs and give stories as hyenas laugh occasionally at your jokes or you will sometimes freeze on your dance moves as a lion roars some meters away.