A lot of small rural towns may not have apartment complexes that would have websites, etc., but there is usually some rental housing. A local realty office or people at the hospital would probably have some helpful recommendations.
Working in a small, rural hospital calls for a lot of flexibility and adaptability. It can be challenging for a new graduate, as you may not have a lot of other nurses around to provide back-up/support (the federal rules for CAH (critical access hospitals) don't even require that they have an RN on-site 24 hrs/day -- however, that doesn't mean that every CAH is staffed that minimally. Many hospitals that qualify and are requlated as CAH look and operate just like "regular" small community hospitals on a day-to-day basis).
I started out my career (back in the Dark Ages) in a small, rural community hospital, and had a great experience. Best wishes for your journey!