I echo the Kyoto thing. Never heard of an applicant to Nagano being rejected (I live in Nagano - the prefecture not the city). It gets pretty cold round here in the winter, but if you want to ski/snowboard this IS the place to come. Vacation time, however, sucks big time. Schools in the prefecture get at most 4 weeks summer vacation, whereas Nagoya schools are probably on about 6 weeks. This used to be because of extra vacation time taken during the coldest of the winter months - but hardly any schools do that anymore - but god-forbid they alter the length of the summer vacation accordingly!
Nagoya is basically never cold. And in the summer it's the hottest major city in Japan. If you enjoy your nightlife, shopping, will miss American food, and want to meet lot's of other gaijin then opt for Nagoya. If you want to ski, study Japanese, enjoy the countryside, if you have a drivers' license and want more of a traditional Japanese experience then go Nagano.
A note Since approximately 80% of Japan's landmass is uninhabitable (in other words mountainous) the largest population groups are to be found in the major cities. 80% of Japanese people do indeed live in major cities - this is the norm. When people, such as myself, refer to a more 'Japanese' experience being available in the rural areas you have to take these statistics into account. Herding cattle across vast plains might be regarded as a true American experience - sitting for hours on a 12 lane expressway during rush hour is perhaps a more accurate representation.