If you want some very cheap but somewhat slow rides around entire Japan get a seishun 18 kippu
>>25641019
If you have over a monthy in Japan you can see more than 3 cities
>>25641058
You can go on a few day rides or stay overnight somewhere for a day or two. JR do a Kanto area rail pass quite cheaply, although Japanese trains are cheap by. For example, Kawagoe, Chichibu, Nikko, Kamakura/Enoshima are all places I'd recommend by train