Here’s a link to the Kenyan Wildlife Service where you’ll find links to all the national parks in the country, including the Nairobi NP which celebrated its 70th anniversary late last year. This is how it describes itself:
“The World’s Wildlife Capital”. A short drive out of Nairobi’s central business district is the Nairobi National Park. Wide open grass plains and backdrop of the city scrapers, scattered acacia bush play host to a wide variety of wildlife including the endangered black rhino, lions, leopards, cheetahs, hyenas, buffaloes, giraffes and diverse birdlife with over 400 species recorded. Visitors can enjoy the park’s picnic sites, three campsites and the walking trails for hikers.”