Yes but you will need to pay extra for a berth or couchette and it comes to about 6000Y per person.
It is only free if the train has seats in it and only a few do. Most only have berths and couchettes - so you will have to pay for those.
Here's one good link for checking out sleeper trains in Japan. There are more free sleeper trains than you think.
http://www.japan-guide.com/e/e2356.html
I don't really recommend it unless you're really pressed for time and wanna save money on lodgings... Japan needs to be savoured, not rushed thru.
As for Toyoko Inn, it's quite nice and has many branches all around Japan. Make sure you get their membership card when u check in, it costs only 800yen but entitles you to 50% discount on sundays and public holidays, and it lasts a lifetime. They have free breakfast, but i got really tired of eating onigiri after a week.
And there are really pros and cons in trying to speak japanese to them. On one hand, if you're not good at it, you're just asking for trouble. They will rattle off really fast and you're very unlikely to catch anything; real japanese ppl DON'T speak as slowly as in anime, movies or tv shows. But if you're at least advanced level (can't remember which JLPT), your japanese may impress them and some of them will really go out their way to help you. Once i made a mistake with a laundry machine and approach a hotel staff in english. She politely stated that my money is gone and can't be helped. I explained again in Japanese and she spent the next 15 mins pleading with her supervisor to get me a refund, which i got. In a restaurant, the staff are more friendly and will recommend good dishes if you speak in Japanese. That said, don't try it unless you're brave enough to capitulate and admit, "gomen, jitsu wa, ore no nihongo wa dame desu.." (or, sorry, actually my japanese really cannot make it)
Takayama is really recommended but it's quite out of the way. The Gassho houses in Shirakawago (2hrs from Takayama, assuming snow doesn't swallow the roads) are one of the more frequently featured pictures on Japanese media (along with Mt Fuji and Kyoto temples).
Tohoku and the central north region can be very beautiful but also extremely challenging due to the sparse transport network and difficulty in travel without good planning or knowing a little japanese.
Actually, there's someone in this forum who is a real expert in Japan travels and i learnt a lot from him when i first started travelling there
