[Kolossus]

Hi everyone. I'm new to this site. There's a lot of helpful info on this site.
I was wondering of some of you could give me some tips or advice for my trip to Japan.

I'll be traveling with my friend.
I was thinking of taking $2000 for me to spend.
Will that be enough or should i take more?
He has a friend in Shinjuku, so he wants to stay there.
We'll be in Japan November 6th and flying back home on November 21st.
What's the weather like around that time?

From what i've been reading on this forum it sounds like Kyoto is really nice.
So i want to visit there. And my friend wants to visit Mt Fuji.

I want to see castle's, temples, historical sites, and some nature sites like maybe lakes and waterfalls.
I want to experience the whole Japanese culture.
And i also want to experience some of the night life.
I want to see and do as much as i can within the time that i'll be there.

Is there any places that you guys can recommend that i visit while i'm there?
Also how much is the Shinkansen from Tokyo to Kyoto?