[Firebird]

You could add a daytrip to Himeji from Osaka, its only 1hour and the castle is huge!
I havent been in Takayama and Yokohama so i cant say anything to those.
Tokyo is worth 5 days,
Homestay´s are always a great experience
I personally found Nagoya not to interesting but we got someone who lives there who can tell you more
Kyoto and Nara together are also good with 5 days
try to get one more day in Osaka and visit Shinmachi (this is in Osaka) to see an oldstyle amusent district

Like i said, Himeji is also quite possible and only 1 hour from Osaka by local train (there a special Rapid for the same price 1500yen). If you get up early enough it can be a half day trip and than spend the evening/night in Osaka.

Have fun!

oh, if you get bored Kobe Harbour is quite nice as are the 2 nightspots on the mountains behind the city.