I don't believe Al Hirt played in any Greenwich Village clubs in 1961, or at least none that anyone's recorded. From the mid-1950s to early 1960s, Hirt and his band played nightly at Dan's Pier 600 at the corner of St. Louis and Bourbon Street in New Orleans.
He most certainly was in New York off and on during this time, as he recorded the albums, Honey in the Horn and Cotton Candy, which were both in the Top 10 best sellers for 1964, the same year Hirt scored a hit single with his cover of Allan Toussaints' tune "Java" (Billboard No. 4), and later won a Grammy Award for the same recording. Both Honey in the Horn and "Java" sold over one million copies, and were awarded gold discs.
Hirt's Top 40 charted hit "Sugar Lips" in 1964 would be later used as the theme song for the NBC daytime game show Eye Guess.