According to the Humboldt Travel Journal, the decision to commemorate Riverside, Iowa as the birthplace of James Kirk was originally intended to act as a tourist attractor. After the success of the first Trek-con, the Council then decided to build a dedicated Star Trek museum.
This phenomenon is the brainchild of Riverside City Council Member
Steve Miller. In March of 1985, Miller suggested to the City Council,
which was looking for a theme for the annual town festival, to
celebrate Riverside as the future birthplace of James Tiberius Kirk,
the infamous captain of the U.S.S. Enterprise on NBC's late 1960s
sci-fi series "Star Trek." The future historical birth, which is set
to take place on March 22, 2228, is also celebrated annually by the
people of Riverside.
"I had read in Stephen Whitefield and Gene Roddenberry's 'Making of
Star Trek' that Kirk was born in a small town in Iowa," said Miller.
"So out of the clear blue sky, I made a motion at the City Council
meeting that we designate Riverside as Kirk's future birthplace."
Deep Space Iowa: The Captain Kirk Museum - Humbold Journal
Prime Timeline (Main canon)
All we know is that Kirk's (original) birthplace was in Iowa. No specific town is mentioned.
Alternate timeline (Abramverse Canon)
Kirk was born on a shuttle in deep space, then raised in Riverside, Iowa next to the Riverside Shipyards where the Enterprise was under construction.
“We’re at the Riverside shipyard inspecting construction of a new
vessel. Shuttle for new recruits leaves tomorrow oh-six hundred.” He
hesitated, then locked eyes one last time with the younger man
standing across from him. “Your father was the captain of a starship
for twelve minutes. He saved eight hundred lives, including your
mother’s and yours. I dare you to do better.” Pivoting sharply, he
headed for the door.
Star Trek (2009): Official Novelisation
Many authors, including William Shatner (the actor who protrayed Kirk in the main canon shows and films) have made mention that Kirk was born in Riverside, Iowa.
“Okay. That’s you, I guess,” she said. “Where are you from?”
“Sounds pretty. Is it a Federation colony?”
Abruptly self-conscious, Jimmy realized he hadn’t added the main part
of his address. He was used to being with people who already knew.
“No… it’s in Iowa.”
Star Trek TOS: Best Destiny
Joseph brightened. “I remember the horses.” They’d gone to a ranch
resort in Iowa near the site of the Kirk family farm, on the outskirts
of Riverside. But the land was now a world heritage park, and not even
the foundations of the house or the barn had remained. Kirk recalled
that, in an earlier time, there’d even been a statue of himself
nearby. But that was gone, too. The old saying was true: Fame was
fleeting. Nor could it compare with the simple joy of riding with his
Star Trek TOS: Captain's Glory by William Shatner