Definitions
1.NounA corner; a nook. A fairy fiddler frae the neuk, [nook] - "Robert Burns", by William Allan Neilson (1917)
2.NounA bend (e.g. in a coast) …the fleet, after exploring the harbours, had doubled the East Neuk, passed safely through St Andrews Bay, and entered the Firth of Tay. --Chronicles of Strathearn (1896) - Rev. John Hunter.