Someday, I really want to visit and explore Japan, but where are the best places to stay when I'm on a budget and don't speak Japanese?
For a first time traveler, definitely should experience Tokyo and other cities in Kanto region, Kyoto, Osaka. There are many English signs and information in major sightseeing spots in these cities, as well as hostels and guesthouses for budget savvy travelers.
However, my true recommendation is rural areas in Japan. Japanese government is trying to make easy to get around for international visitors in such areas, so hopefully there will be less language barriers very soon. Lots of nature, great food, beautiful sights are in the rural areas!