Interestingly, Hyperdia does not even recognize Nihonmatsu as a destination although there IS a JR Nihonmatsu Station - strange. To get there by train, you would depart either Koriyama or Fukushima on the JR Tohoku line local train.

I can't actually recommend anything as I have never stayed there, but:

The only listings I found on my booking websites for Nihonmatsu were some VERY expensive, high-end resort/onsen/ryokan in the hills outside of the town. Most of those are 15 to 45 minutes by car or bus from the town.

If you are looking for something a bit more reasonable, I'd think you should look in either Fukushima or Koriyama, which are both around 20 minutes by local train from Nihonmatsu. One example of a recent search:

http://www.japanhotel.net/data/pref/...Area=FUKUSHIMA .

Another:

http://www.japanhotel.net/data/pref/...&Area=KORIYAMA .

That is just one booking site. There are others.

JR