Apartments For Rent Grafton County Nh . In addition to the rent cost, you need to also account for costs of basic utilities consisting of. 452 north shore road, grafton county, nh 03241. 148 Washington St, Conway, NH 03818 Apartments Conway, NH from www.apartments.com Compare rentals, see map views and save your favorite apartments. You searched for rentals in grafton, nh. Search 13 rental properties in grafton county.