Time and Again by Jack Finney
Amazon Link: Time and Again
Commercial artist Simon Morley is chosen by a secret U.S. government project to travel back in time to 1882 New York City -- just to prove it can be done and to observe. He enjoys the sights of the city at that time: still much farming on Manhattan, the Dakota and Museum of Natural History standing pretty much alone, the arm of the Statue of Liberty standing by itself in Madison Square, and many other things. But he also falls in love with Julia Charbonneau, who is engaged to a brusque and brutal man named Jake Pickering. It turns out Pickering has some sort of blackmail scheme going, and Si must decide whether to meddle with events.
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