For Gifu/Nagoya, it really depends on what kind of lifestyle you want, but I'd say anywhere from about ¥120,000 to ¥200,000 a month if you're single, or ¥200,000+ for a couple.
Approximately correct to my experience. Note that foreigners will blow past the low end if they are not willing to live like Japanese people, particularly with regards to food budgets (with some exceptions, food like you're used to is systematically more expensive than Japanese food) and rents (middle-class Americans would often not tolerate the kinds of housing arrangements young Japanese people do).
Lifestyle choices are the main variable in cost of living...