If you mean remote as in remote within Orkney then the areas to try are Deerness and Birsay and Orphir and South Ronaldsay.
http://www.visitorkney.com/accommodation.html has a link to search the VisitScotland site for your requirements (http://www.visitscotland.com/accommodation/accommodation/?view=Standard) and another to download a .pdf of accomodation in Orkney (http://www.visitorkney.com/download.html).