No offense, Galt, but the OP was asking just about, NYC, not the many burgs you have known.
And here in NYC there is only ONE ice cream truck jingle by which all others are judged: Mr. Softee. Sure there are others, but none can touch the perennial, pervasive – and utterly, utterly annoying – Mr. Softee:
Deedelee deedelee deeddelee dee, dink da-dink da-dink dink… and over, and over, and over…
That being said, here are few more facts I found on the web:
“Les Waas has been President of Waas, Inc., an advertising agency for 45 years and is owner of New Sounds, a creative service specializing in jingles and humorous commercials, and winner of most major creative awards. He has performed voices in hundreds of commercials for radio and television. Les has written and produced 973 jingles for such advertisers as “Mr. Softee” (heard on thousands of ice cream trucks)…”