The movie theater exterior is The Fox Village in Westwood, California.
The sweater in the store window is advertised as coming from Alaska, the 49th state. Alaska was admitted to the Union as the 49th state in the U.S. on 3 January 1959, just a few months before this episode aired. Hawaii, which would become the 50th state, had not yet been admitted. That event would not occur until August of that year.
The marquee on the movie theater is advertising the showing of Tammy and the Bachelor (1957), starring Debbie Reynolds. The movie's actual release to American theaters was in the summer of 1957, almost two years prior to the airing of this episode.