The Japanese alps are divided into three sections: North Alps 北アルプス, Central Alps 中央アルプス, and the Southern Alps 南アルプス. All of the sections have plenty of mountain huts along the mountain trails, but the North Alps have the most. Kamikochi 上高地 is probably the most popular spot for backpacking, making it the most crowded. You can do overnight to several nights in the area. Kamikochi is also accessible by public transportation, but is fairly expensive.
The central alps are nice, but not as developed.
Ontake-san is a volcano located between the North and Central Alps and is accessible by train from Matsumoto by going to Kiso-Fukushima and then from there by bus. It's a fairly short hike to get to the top, but there are lots of places to see (including the highest pond in Japan) and great views of all of the alps--you can stay in mountain huts here too. The prices range from about 4000 to 8000 yen a night. You can read more at my
blog.
You can buy maps that are easy to read at any of the big bookstores in the cities. They divided into small sections, so make sure you get the one you are looking for. They are very informative though: show times, locations for water, and mountain hut locations.