Bradbury does not give us a precise time and place setting because he wants us to be able to apply it to any time and any place in the not too distant future. We know it is not in the current time when the story opens with a description of Montag's job of burning books. That isn't something we see in our present day world. Other indications that the story is set into the future is the technology mentioned: the Mechanical Dog, the "silent, air-propelled train", the wall television screens, the fast cars. When Clarisse talks to Montag and describes the speeds at which people drive and how billboards had to be made extra long to accommodate the high speeds, we also know that this is the future, but not too far into the future because there are still memories of a society similar to our current day. The place is a large city, except for the end when Montag joins the book people in the remote countryside. We know it's a city because of the large numbers of people on the trains and on the streets. Also, an enemy is much more likely to bomb a large city than it is to bomb a small city.