I don't really know about cheap option, so maybe it's not helping,
but I just want to tell you about what I have had before for my trip in Japan
It was like 3 years ago so I'm not sure if I remember it correctly..
I used a special ticket called 18 kippu (jyuu hachi kippu).
http://www.jreast.co.jp/e/pass/seishun18.htmlIt costs 11,850 yen for 5 ticket, and 1 ticket can be used for 1 person in a day.
In my case, I went to 4 cities in 3 days.
I wasn't really speak Japanese well also when I did the trip, but it was OK because I planned the trip by checking the train schedule here:
http://www.hyperdia.com/en/I printed the pages and it really helped me, because I didn't need to see the train map (but if you go to big cities, there's big chance you can get romaji/english information)
Also, there are a lot of cheap hostels/ryoukan (like 1,800-2,000 yen a night). In Nagoya, I stayed in a very nice ryoukan that only costs 2,000 yen a night, the owner can speak English and he was really nice that he picked us from station and took us to station again the next day, and refused a tip.
For food, just eat simple onigiri+milk from mini market for breakfast. The total will be about 250~300 yen..
Take lunch and/or dinner in family restaurant or a place like sukiya. It costs about 500 yen for sukiya, if I remember it correctly.. and about 1,000 yen for family restaurant
but still, I think it will be a waste if you don't try to eat at a nice restaurant once or twice, and it might be costs about 2,000 yen a time :)