Fairfield is several miles south of Cedar Fort. It was the home of Johnson's Army after the Utah war in 1857. While the army was in residence, it was known as Frogtown. The name was changed to Fairfield in 1861, which I believe was a great improvement. The army left with the beginning of the Civil War. Now it is the home of the Camp Floyd state park. They have pony express reenactments there every year.
They must be anticipating great growth sometime in the future because their town sign was miles away from any building. We could barely see the little town in the distance, but we could get up close and personal with the bones at the foot of the sign.
p.s. Harmony we finally found the Pleasant Grove sign a day ago. Thanks for your help!