The basic details of Pandit Nikhil Banerjee's life are well-known, and I will only provide a brief summary here. I have also added some links to further biographical information and reminiscences which help fill out the picture..
Nikhil Ranjan Banerjee (or Bandopadhyaya) was born 14th October 1931, one of nine children. He is usually credited with taking up sitar at the age of five, but a family member reminiscence from grand niece Monica Sarkar relates, it was from the age of four his talent showed. By nine he was said to have become such a prodigy that he was employed by All India radio. He studied under at least three sitar masters, Mushtaq Ali Khan, Birendra Kishore Roy Chowdhury and Radhika Mohan Maitra before at the age of sixteen he became a disciple of Allauddin Khan. He was also influenced by singer Amir Khan, and wrote of his admiration in a piece for a memorial project Music of the Soul. (That page also contains a link to a recording of Amir Khan being "inteviewed" by NB).
From 1947, after a difficult start, Nikhil Banerjee studied under Allauddin Khan and later also from Allauddin's children, Annapurna Devi, but principally, especially after Allauddin's death, from Ali Akbar Khan.
Nikhilda's first foreign tour came in 1955, when he was among a cultural delegation from the Indian government to Poland, Russia and China. Later he toured Afghanistan, Nepal and other places, but from the mid-sixties he regularly toured Europe and North America. He began spending several months in California, where Ali Akbar Khan had established a college of music, although he professed not to enjoy teaching.
He also remarked he did not much enjoy studio recording, but for much of his career the recorded output was from the studio rather than from live concerts. This changed after his demise.
During the 80s his heart started failing and he succombed on January 27th 1986 at the age of 54, just a couple of days after his last performance at Dover Lane Music Conference, Kolkata. The recording of his Darbari performance at that concert stands as a poignant reminder of his stature as an artist. He was survived by his wife and their two daughters.
More insight into his life can be found in many places on the web, including Wikipedia, and you will find some other links on this site. Also the interviews throw much light on his life under his gurus and his attitude towards his music.
A biography in Bengali was published by Ananda Publishers, Kolkata in 1994 - Swapan Bandyopadhyay(Banerjee): "The Strings Broke Long Ago" ("Taar
Chhnide Gechhe Kobe") but I have never seen a copy. The only comment on this I have seen said "..makes excellent reading, albeit in a slightly overdramatic style."