Chic Apartment Accommodation. Quest Newmarket offers a range of spacious modern accommodation for the business and leisure traveller. The studio one two or 3 bedroom apartments are tastefully furnished with well equipped kitchen and laundry facilities. Free Wi-Fi and movies, Sky Sport in HD. Quest Newmarket offers a secure home away from home experience whether staying for just one night a week or longer. Just a minute from the best shopping in NZ and not more than 10 from all the major Auckland entertainment venues.