Houses And Apartments For Rent In Morehead City Nc . 2708 homes dr, morehead city, nc is a single family home that contains 1,146 sq ft and was built in 1941. Freshly painted, new appliances, close to downtown, parks, playground, tennis courts, restaurants, promise land market, shops and bogue sound access for swimming. Carteret Court Apartments Morehead City, NC from www.apartments.com 541 n 35th street, morehead city, nc 28557. $1,950 | 3 beds | townhome for rent. The average home rent in morehead city is $2,138.