Fist time in Japan

Hey guys I am travelling to Japan for first time(solo traveller) from December 18-23. I am planning to visit Tokyo and Kyoto. What should I go see in Tokyo/where should I stay. I am planning on staying in hostels or ryokans. I am trying to see both the modern and historical side of Japan. What do you guys recommend for someone travelling alone? Thanks!

Which airport do you arrive at? At what time?
Which airport do your depart from? At what time?

With such limited time just split your time between Tokyo and Kyoto.

If you want to stay in a ryokan do so in Kyoto. If you wish to keep the budget down the spend one night in a ryokan in Kyoto and for your other nights in Kyoto choose a hostel/guesthouse.

For Tokyo pick places of interest from here:-
http://www.japan-guide.com/e/e2164.html
There are some suggested daily itineraries here but feel free to make your own:-
http://www.japan-guide.com/e/e3051.html

I usually think Tsukiji Fish Market is an interesting place to visit, although the Tuna Auction is likely to be closed when you visit.
http://www.japan-guide.com/e/e3021.html

Christmas illuminations:-
http://www.japan-guide.com/e/e2303.html

For Kyoto pick from here:-
http://www.japan-guide.com/e/e2158.html
Daily suggestions:-
http://www.japan-guide.com/e/e3950.html
Kinkakuji is commonly visited:-
http://www.japan-guide.com/e/e3950_northern_kyoto_half.html

If you want to save on transport then consider overnight buses between the two.
http://www.japan-guide.com/e/e2366.html

Alternatively, a 7-day JR Pass is likely to pay off but must be purchased in your home country before you come to Japan.
http://www.japan-guide.com/e/e2361.html

Kyoto access:-
http://www.japan-guide.com/e/e2363.html

Enjoy your trip!

You BADLY need to read a couple of guidebooks and also need to check the tab A-Z at the top of this page....
Only YOU can decide what is interesting you or not.

For example, when I travel on my own, I am interested in buildings old and new, in transit (trains, trams, buses etc.), in big and small stores etc. (but seldom buy souvenirs) etc.

I'll talk to someone in a train or coffee shop but am not interested at all in a friendship or sex.
I eat simple food and don't drink alcohol at all..yet I have a good time anywhere I go.

What are YOUR priorities???