Omaha, Nebraska snows during early winter to spring. But, snow isn't emphasized an important aspect of the book. Omaha is on the Missouri River and is close to the Iowa border. It is the largest city in Nebraska. The city seems to be split up between the downtown area (more stores and city like) and the town area (more towns and country side) I assume the novel takes place more in the town area because of the smaller population and because the book never references any buildings or city places.
Two of the items that help time stamp the book is a tape player (1963) which is what Park listens to on the bus and later gives it to Eleanor to "experience" music. Another item is a Chevy Impala which was made from 1958-now. The car was supposed to be a gift to Park once he gets his drivers license (and learns to drive manual by his dad).