The town of Asahigaoka is not explicitly based on any single real location. Of course, some location scouting in the countryside was performed for the sake of realism.1 Most anime these days engage in this activity (called "location hunting" / ロケハン) when appropriate - e.g. when they are set in modern Japan or something that looks like it.2
That said, the school the students in Non Non Biyori attend is apparently based on a real school: Ogawa Elementary's Shimosato Branch School3 in Ogawa, Saitama.4
1 See this blog post (JP), and in particular this image (JP), taken from an interview with people on the production staff.
2 Of course, some shows do use full-on model cities, e.g. Ano Hana and Ano Natsu de Matteru.
3 I believe I translated that well enough, but school nomenclature confuses me at times - the name in Japanese is 小川町立小川小学校 下里分校, lit. "Ogawa-machi Municipal Ogawa Elementary School, Shimosato Branch School".
4 For details and comparison shots, see e.g. this blog post.