Craig began his musical career in the early 1960s as the rhythm guitarist in the teenage surf band The New Dimensions.

During the mid-1960s, Craig played with a few bands in and around the Sunset Strip. He did a short stint with The Eastside Kids, where he first met Denis Lambert. 

In late 1967, he and Denis formed the duo Lambert & Nuttycombe

They released their first album on A&M Records in 1970, produced by Glyn Johns, David Anderle, and Chad Stuart. "At Home" was recorded at their Sausalito, California residence with just their two guitars and vocals.

"As You Will" was their follow-up on 20th Century Records in 1973. Keith Olsen produced and featured some exceptionally talented Los Angeles musicians, his father being one of them. Shortly after completing the album, they would go their separate ways.

Craig would travel to England for his first solo album for A&M in 1978. "It's Just A Lifetime" was produced by Glyn Johns and Andy Fairweather Low. 

Towards the end of 1979, inspired by his friend (and photographer) Ethan Russell, he left his hometown of Hollywood for Carmel Valley. He put the music business on hold to go live and work on Ethan's parent's beautiful ranch. He stayed there for a few years while he continued to play and write but put music as a career aside. 

After his time in Carmel Valley, he moved south to San Luis Obispo, where he still resides. 

In 1990, Craig returned to recording with his second solo album, "My Own Beat." 

He would record several more solo albums before joining the band Café Musique. They mixed together folk, gypsy, swing and tango styles to become one of the more exciting bands on the coast of Central California.