Fujilakes or not?

Hi friendly advisers! We're a group of 3 students who'll be backpacking Japan in June 2008.
We're intending to follow the suggested itinerary by japan guide.com which is the following:

Day 1: Arrive at Narita Airport, and spend the remaining day in Tokyo.

Day 2-4: Spend two full days in Tokyo and one day in nearby Kamakura.

Day 5: From Tokyo, make a day trip to Nikko.

Day 6: In the morning, travel from Tokyo to Takayama (4.5 hours) and spend the afternoon and evening exploring Takayama.

Day 7: Leave Takayama in the afternoon for Kyoto (3.5 hours) and spend the evening exploring Kyoto.

Day 8-11: Spend two full days in Kyoto and one day each in nearby Nara and Osaka. Nara and Osaka are easy day trips from Kyoto.

Day 12: In the early morning, travel from Kyoto to Hiroshima (2 hours) and visit the Peace Park. In the afternoon, continue to Miyajima and overnight there.

Day 13: Leave Miyajima around eleven for Himeji (2 hours). Spend the afternoon exploring Himeji Castle. Return to Tokyo in the evening (3-4 hours).

Day 14: Depart Japan from Narita Airport.

However, we're thinking of visiting Fuji Five Lakes, which is not suggested in the itinerary.

Any suggestions on which of the above places (e.g. Kamakura or Nikko) should we forgo, to visit Fuji Five lakes?

Also, are there any value for money hostels or budget hotels to recommend for accommodation?

Thanks a million in advance!! =)

As you will visit Kyoto you might skip Kamakura. On that day you can make an easy daytrip to Hakone and the round tour there. On a clear day nice view of Fujisan.