The Moon Landing (1865)
To be fair, a lot of fiction imagined what it might be like if human beings were capable of flying to the moon. But From Earth to the Moon, a 1865 novel by author Jules Verne, got closer with more of the details than most.
Sure, the general premise was kind of silly—a giant cannon fired a manned projectile into space—but he wrote about the weightlessness that astronauts experienced, something an author in the mid-19th century would have no way of knowing.
Verne also predicted that there would be three astronauts on that first moon mission—though his astronauts never actually walked on the moon—and that Tampa, Florida, would be the launch site. (The Apollo 11 mission launched from the Kennedy Space Center, in nearby Orlando.)