Jimi Hendrix introduced his post Experience group to the world with pairs of New Year's Eve and New Year's Day concerts at the Fillmore East in 1969/70.  The Band Of Gypsys double live album released on March 25, 1970 featured songs culled from recordings of all four sets, but most were from the New Years Day concerts.  There were no set lists. Hendrix called out audibles to bass player Billy Cox and drummer Buddy Miles.
Other first day of the year goings on over the decades include the Beatles auditioning for Decca Records 1/1/1962 and getting passed over by the label in favor of Brian Poole and the Tremeloes. 
Journey released Look Into The Future and Jimmy Buffett put out Havana Day on New Year's Day in 1976.
VH1 launched on 1/1 in 1985.
In 1995, an estimated crowd of 2 million+ filled the beachfront in Rio for a Rod Stewart performance.