I did a cross country trip, in two weeks, with the JR Green pass because I had a large backpack (and thought I would need the extra leg room) but a eregularf pass would work.http://japanrail.com/index.html
(I suggest you read whole website, if you havenft already)http://japanrail.com/JR_tourismlinks.html http://japanrail.com/JR_timetableandfare.html
(couple key sections of website that I suggest)
Kagoshima, Nagasaki, Hiroshima, Kyoto, Chiba and Sapporo are couple of the cities I visited, I missed Shikoku island, and stayed in a new hotel each night/city. The only problem with my trip, staying at new hotel every night, is I was running around too much between etourist sitef and finding hotel to fully enjoy my trip.
I suggest 3 or 4 base sites (Hiroshima, Osaka, Chiba, Sapporo). As for hotels I stayed in Tokyo-Inn, Comfort inn, etc, at 6800 yen ($60-ish Canadian) per night (single person), another cheap option is hostels.
The only other way to make your trip as inexpensive as possible, is to plan your butt off. Find the etourist sitef that are interest of you, in said city, and find location (address is best) in relation to the train station (bus terminal, witch ever you choose) and decide if the distance is walk-able for you and your girlfriend. Otherwise see if there is another train stop, local train (still on JR line), that is closer.
Have a safe trip