There are a number of approved Hospitals that offer COVID-19 tests in Kenya. It all boils down to how long you are ready to wait for the results.
Kenyatta University Hospital is the most affordable. It costs Kenya Shillings 3,000 for COVID-19 test. It releases test results from 1 to 3 days.
If you are traveling and want 24 hours results, then Nairobi West Hospital is your best choice. It charges Ksh. 6,000.
Kenyayote has published a list of hospitals that offer covid-19 testing services in Kenya and their cost here https://kenyayote.com/cost-of-cheapest-covid-19-testing-centres-in-nairobi-kenya/