It depends on your budget & the lenght of your trip - but i highly recommmend that you get a JR PASS to make your long trips cheap, easy & flexible as well.
Recommends cities may be
HAKONE - FUJI
KYOTO - Must see if you do have a JR PASS
These may be ok , but if were you and i do have Jr PASS open for 2 weeks i will travel to all the big cities that have the bullet train (shinkasen ) in it .
I hope my suggestiom may help
Good luck and yokoso