Hakone and Takayama

we are planning to be in japan on april fo 13 days neto
is it worthwile to be in Hakone for 2 night? is it possible to go from Hakone to Takayama in the afternoon after spending the morning in mt. Fuji? how we get from Hakone to Takayama
the original plan is:
1 tokyo
2 tokyo
3 niko and back to Toyo
4 Tokyo
5 going to Hakone sleeping in Hakone
6 Hakone sleeping in Hakone
7 going to Takayama sleeping in Takayama
8 takayama sleeping in Takayama
10 going to kyoto
11 kyoto Nara and back to kyoto
12 kyoto Hiroshima Kyoto
13 kyoto
14 fliying back home

i don't know if worthwile to stay 2 night in Hakone or to live in the afternoon to Takayama and so we can spend another day in Kyoto
how much time it takes to get from Takayama to kyoto?
thank you all if you can advice me
Nira

Is it worthwile to be in Hakone for 2 night?

Yes. You will be there for two nights, but wil actually spending only 1.5 days or less in Hakone, which is good amount of time to enjoy Hakone.

is it possible to go from Hakone to Takayama in the afternoon after spending the morning in mt. Fuji?

What do you mean spending time at Mount Fuji? It is possible to take a look at the mountain from Hakone or from the train between Hakone and Takayama. If that is not enough, you could take a look at it from Gotemba and then continue to Takayama via Nagoya. Or do you wish to go to the Fuji Five Lake region? In that case, your route could look as follows:

Hakone - (buses) - Lake Kawaguchi - (bus) - Kofu - (train) - Matsumoto - (bus) - Takayama

You need to check the bus timetables carefully, because service between Takayama and Matsumoto is not so frequent.

how much time it takes to get from Takayama to kyoto?

Here you go:
http://www.japan-guide.com/e/e5908.html?aFROM=2158_5900

Hi Uji
first thank you for the answer
another quastion concerning Hakone. what did you mean when you say that i'll be in hakone only 1.5 days. it is close to Tokyou and we are planning to go there by the shinkansen train
Nira

You are right. If you leave Tokyo early in the morning, you will have two days in Hakone.

so perhaps it's enough to spend only 1 night in hakone?
Nira

so perhaps it's enough to spend only 1 night in hakone?
Nira

Hakone - (buses) - Lake Kawaguchi - (bus) - Kofu - (train) - Matsumoto - (bus) - Takayama

I doubt this schedule is worth trying in a day, sounds very hectic, though it's possible.

Hakone Togendai 6:40--bus--7:15 Gotemba 8:10--bus--9:23 Kawaguchiko 13:00--bus--14:20 Kofu 15:24--JR Azusa--16:26 Matsumoto 17:10--bus--19:30 Takayama

perhaps it's enough to spend only 1 night in hakone?

I think so. You might want to spend the spare day on Kawaguchiko area.