Trip in november

I'm going to Japan for the first time in november, I want to visit Tokyo, Kyoto, Nikko, Kamakura, Nara, and perhaps Mount Koya. I was thinking I could do all this in 12 days, 5 nights in Tokyo, 4 in Kyoto, and I just don't know where to spend the 2 remaining nighst ¿Should I stay more nights in Kyoto or Tokyo? I wouldn't like to go further than Kyoto.I was wondering if it would be best to leave Tokyo till the end as my plane leaves from Narita Airport, or is it easy to go from Kyoto to Narita airport? Also I'm traveling alone, is it a good idea to do that in Tokyo or is it dangerous?

I'm going to Japan for the first time in november,

What exact dates?

I want to visit Tokyo, Kyoto, Nikko, Kamakura, Nara, and perhaps Mount Koya. I was thinking I could do all this in 12 days,

Sounds ok.

5 nights in Tokyo, 4 in Kyoto, and I just don't know where to spend the 2 remaining nighst

Depends on your interests. Maybe overnight in Mt Koya?

¿Should I stay more nights in Kyoto or Tokyo?

I would pick Kyoto, but you spend two days away from Tokyo seeing Nikko and Kamakura so you could pick Tokyo too.

I wouldn't like to go further than Kyoto.

Ok.

I was wondering if it would be best to leave Tokyo till the end as my plane leaves from Narita Airport, or is it easy to go from Kyoto to Narita airport?

It is relatively easy assuming your plane leaves in the afternoon/evening. Shinkansen from Kyoto to Shinagawa/Tokyo Station then Narita Express from there to Narita.

Also I'm traveling alone, is it a good idea to do that in Tokyo or is it dangerous?

Tokyo in general is a very safe city and there are many single travellers. I would not worry.

You may wish to consider a 7-day JR Pass for your trip to Kyoto and back. You could also use it to go from Tokyo to Nikko and back, and Tokyo to Kamakura and back. I would activate so that it is valid for both those trips and the trip to Kyoto and back. ie. the last 7 days of your trip.
http://www.japan-guide.com/e/e2361.html

Note that Kyoto gets busy during November due to autumn colours (Koyo) so book in advance.
http://www.japan-guide.com/e/e2014.html

Enjoy your trip!

I was thinking about Mt. Koya but I haven't been able to find the right place to stay there, also I was thinking that perhaps it wasn't wise to go there in november, as it might be a bit too cold. Thank you for the advice, I think I'll reserve everything next week.