Coming to accomodation yes you can get hostel/hotel in tokyo or kyoto
for as cheap as JPY2000 - JPY 5000/night .
This accomodation are self catered with almost everything from kitchen to laundry service, free internet access plus alot free service making your stay a wonderful one .
Coming to transportation we recommend a the following options
JR Pass - For nationwide travel service
Japan Bus Pass - For Overnight Bus
Travelling only in tokyo may be you can consider the Metro day pass
In the Kansai region, travelling through kyoto,osaka, kobe ,nara ,wakayama,
you might want try kansai Thru Pass
City Bus in kyoto - Get the chance to see all the sightseeing spots in this wonder old capital of japan .its just amazing trying this bus also dont forget you can rent bicycles from the kyoto hostel another great way to see this great historic city of kyoto .
Its always good to find the best way to save money in travelling so we recommend and give you the best tips to save money in travelling in japan.
There might be other options but these are some of the recomended ones.
Stay tune for Japan Budget Travel Tips -2 - Eating and partying coming soon .Yokoso (Welcome ) to japan and do enjoy your vacation