Cheap transportation can sightseeing Tokyo to Fukuoka?

Question:

Landed Tokyo on 28th Aug 2011. Have 1week to travel to Osaka, Narita, Fukuoka and return.
1) What is the cheap transport from tokyo to south and return, any ticket pass to buy. How much different Shinkansen and bus?
2) Hostel for backpacker any link hostel that connect every places like XBase hostel in Aust and NZ.
3) What is temperature and season like
4) Sighseeing to Fuji but not climbing.. where should i start? From Tokyo or after returning from Fukuoka.

Answer:

1 week to crisscross the country and sightseeing Mt. Fuji!

I recommend you research getting the JAPAN RAIL PASS. A one week version costs 28300 Japanese yen, you need to purchase it before you come to Japan from a travel agency. It pays itself off especially for the amount of travel you want to do. I recommend dropping the trip to Mt. Fuji. On a clear day, you should be able to see Mt. Fuji on the right side of the Shinkansen train from Tokyo-Osaka (left side on the return)

It will be summer, hot weather but near the end of Summer.