What is the significance of Neddie's visit to the public swimming pool as opposed to the private ones?
Neddy Merrill's journey through the pools of his suburban town is meant to parallel a man's journey through life. When he starts out, he is described as youthfully middle aged, athletic and prosperous. It's no wonder that he is so at home in the private pools where he begins. Notice the tone and mood of the story here. It is faster paced and the tone is definitely upbeat, meant to parallel a man's youth. Neddy is warmly welcomed and thoroughly enjoying himself. If you pay attention as the progresses though, this slowly begins to wane.
Things really change for Neddy, however, when he crosses the highway and decides to enter the public pool. At this point of the story, the day becomes darker and colder and the pacing of the story slows down considerably. This public pool is a place he had previously avoided, preferring to keep company with "his own kind". But reality begins to intrude on the fantasy that Neddy has built. Neddy seems unprepared and exposed. Things are thrown at him, he is unwelcome, and his journey becomes unpleasant and depressing.
Ultimately, crossing that highway represents Neddy moving from the naivete of youth to the reality of adulthood. He is forced to face the consequences of poor choices at the end of his journey when he returns home, only to find it locked and empty.