Apartments For Rent In Downtown New Bern Nc . 216 lombardi cir, new bern, nc 28562. Currently, the average rental price for a 3 bedroom apartment for rent in downtown new bern, nc is $1275. 710 Craven St, New Bern, NC 28560 Apartment for Rent in New Bern, NC from www.apartments.com Downtown new bern is located in the central part of new bern, nc. 514 national ct dr new bern, nc 28560. A rental apartment unit in this residential area is on the average $1,228.