You could have a, say, generic 1950s era mini-set on the left of the stage and the "regular" set on the rest of the stage. The 1950s set could be blacked out when not needed and vice versa for the "regular" set.
Or, check out the play "The Time Machine" based on a H G. Wells story. This young Steampunk guy from the 1800s or so invents a time machine and goes to the future (the 1950s, at least when we produced it at our high school). There are scenes in both eras in the play. Good luck.