If you don't have any problems with setting up base 13 kilometres outside of the city center, consider the suburb of Aberdeen. This area has 80 options available, such as Jurys Inn Aberdeen Airport and Aberdeen Douglas Hotel.
For some alternatives, look at the Rox Hotel and the DoubleTree by Hilton Aberdeen City Centre. They are 13 kilometres and 14 kilometres respectively from the main center. If those two don't meet your needs, try the Skene House HotelSuites-Rosemount or the Bauhaus Hotel.
The nearby localities of Aberdeen and Raemoir are definitely worth exploring. Aberdeen is 13 kilometres to the north of Newtonhill, while Raemoir is 20 kilometres to the west. Hotels and apartments in Aberdeen are The Craibstone Suites and Skene House HotelSuites - Whitehall. The Burnett Arms Hotel and Tor Na Coille Hotel & Restaurant are some of the ones in Raemoir.
Hotels in Newtonhill start at AU$45 per night. Prices and availability subject to change. Additional terms may apply.