Nick was raised Roman Catholic and played football for Cathedral High School, where a plaque honoring him as a "Hometown Hall of Famer" was unveiled in 2012.

In 1985, his son Marc suffered a spinal cord injury making a tackle for The Citadel, rendering him a quadriplegic.

[4] Nick became the public face of the group that founded the Miami Project to Cure Paralysis, now one of the world's leading neurological research centers.

As a senior in 1961, Nick led the team with 74 tackles as the Irish co-captain and was rewarded with 2nd-team All-America selections from UPI, TSN, and the Football Coaches' Association.

The following year, Buoniconti helped Boston capture the 1963 AFL Eastern Division title.

With Boston, Buoniconti appeared in five AFL All-Star Games, and recorded 24 interceptions, which is still the seventh-most in team history.

His 32 career interceptions rank him third all-time among NFL linebackers.His interception of Billy Kilmer late in the second quarter of Super Bowl VII set up Miami's second touchdown, which proved to be the clincher in the Dolphins' 14–7 victory over the Washington Redskins to complete the 17–0 season.

On November 18, 1991, Buoniconti was enshrined on the Miami Dolphin's Honor Roll at Hard Rock Stadium.

As an agent, he represented some 30 professional athletes, including baseball players Bucky Dent and Andre Dawson.

In a televised interview on the Comedy Channel toward the end of 1990, when asked his reaction to the last two undefeated teams of the season suffering losses the same Sunday, Buoniconti, indicating his cheerful countenance, told Night After Night's Allan Havey, "You know, I think this smile might just stay permanently on my face.

[8] He was one of at least 345 NFL players to be diagnosed after death with CTE, which is caused by repeated hits to the head.