City at World's End by Edmond Hamilton

The pleasant little American city of Middletown is the first target in an atomic war - but instead of blowing Middletown to smithereens, the super-hydrogen bomb blows it right off the map - to somewhere else! First there is the new thin coldness of the air, the blazing corona and dullness of the sun, the visibility of the stars in high daylight. Then comes the inhabitant's terrifying discovery that Middletown is a twentieth-century oasis of paved streets and houses in a desolate brown world without trees, without water, apparently without life, in the unimaginably far-distant future.