A secret "utopian" city hidden in Africa matches "The Lion of Comarre" (1949) by Arthur C. Clarke, but its ISFDb entry doesn't show it being anthologized in English outside of The Lion of Comarre and Against the Fall of Night before 1990.
There's a summary on the Variety SF blog that, while it dwells overly much on the first parts of the stories, describes:
Man & the lion reach Comarre - a closed environment - with entry gate open but no one around. Leaving lion there, Richard will go on adventure through the city. Passing through magical transfer gates popular in later science fiction stories, he will reach the interior. A bit baffled, then escorted by a robot to a chamber where he will go to sleep induced by some kind of force fields. And get into eternal pleasant dreams. Comarre apparently can read your mind remotely, figure out what you like, & then give you the right dreams!
But Richard is strong willed. He manages to get out of dream. Makes robots show him around. Awakens a sleeper or two who are angry at him to have awakened them! Figures out Comarre is evil. Bugs robots. Ends up in a sort of control room. Is prevented by a robot that is sort of master maintainer - and not the only one. I don't recall how lion got in to this control room, but he will restrain the robot from interfering with Richard who is hell bent on destroying Comarre.
The story was originally published in Thrilling Wonder Stories, August 1949, and can be read at the Internet Archive.
