The easiest and most economical way to travel around Japan, if you’re on a tourist visa, is to buy a ‘Japan Rail Pass’ before you arrive: http://www.japanrailpass.net/eng/en001.html. The cost of a 1 week pass is about the same as a single one way fare between Tokyo & Osaka, so the more you use it, the more economical it becomes. If you’re willing to travel slowly over night or simply to get up early and travel from a single ‘base’, you can also save on accommodation. The only other cheap transport is the ‘highway’ bus system, but this is slow and you really need to like cramped, often crowded buses.
For accommodation, Youth Hostels & cheap hotels are available. If you or a friend can read Japanese, it’s best to look for hotels on Japanese websites (eg mytrip.net) as prices are often lower than for the same hotels advertising in English. In Hiroshima, you’d be looking at ¥5000 a night or so. Some students stay at 24-hour internet cafes or saunas when they travel, but it’s probably not a good idea if you’re travelling alone.