I was a big fan of Your Hit Parade, which was on at 10:30 on Saturday nights, if I recall correctly. My cousin and I would call each other during the day and try to predict what the Top Seven songs would be that week. It was fun to see how many different settings they could come up with for a song like "Harbor Lights," which had a long run in the Top Seven. The songs from Broadway shows that were big commercial hits back in the 50's were indeed
from the shows you mention: "Stranger in Paradise" (Kismet), "Hey There" and "Hernando's Hideaway" (The Pajama Game), "On the Street Where You Live" (My Fair Lady) and "Standing on the Corner" (The Most Happy Fella).