Need help with trip!

Hi guys, My 30th bday is just around the corner (July 5th) and i wanted to do something amazing. So I decided to go to Japan! I am doing this trip independently with my boyfriend and was going to follow an itinerary created by a travel agent that we decided not to go with last minute.
The program consists of:
3 nights in Tokyo
1 night in Matsumoto
2 nights in Takayama
2 nights in Kanazawa
4 nights in Kyoto
My question is should we extend our stay in Tokyo, spend a night somewhere on our route to Kyoto and then just take day trips from Kyoto? I was thinking of visiting Nara, Himeji, Osaka, and possibly the bamboo forest in Arashiyama. I am dying to see a sumo tournament which in July takes place in Nagoya starting July 13th. I would also love to see some Gion Matsuri (Yoiyama) festivities which should take place July 14th-July 16th.
We are going to be in Japan from July 4th leaving July 16th. Do you guys have any suggestions for me? I need to start booking hotels!! I also want to see Mt Fuji. Should that be done as a full day trip or is it not worth spending so much time on since the snow on top of it will be melted and it will just look like a mountain haha : ). Thanks!!

Yes Kyoto is a good base for day trips to Nara, Himeji and Osaka. Even the visit of the sumo in Nagoya you can make as a day trip from Kyoto. But expect the hotels in Kyoto being full or heavily booked during Gion Festival. So as an alternative a good base can be the ShinOsaka area, too. In July it is very difficult to see Fuji san, because of the many clouds. You can either join an organized day tour or you can do Hakone by your own, see under travel - Tokyo - Hakone. Calculate by using hyperdia.com what train costs you will have. Will you return to Tokyo to fly out from Narita or do you leave from an other airport? It may happen that a 14 day JR Rail Pass comes cheaper than single rail tickets.

First of all, your "Tokyo, Matsumoto, Takayama, Kanazawa, Kyoto, Nara, Himeji, Osaka, Nagoya and Mt Fuji in 12 days" plan is so packed that you should pick out more selected distinations. At the same time, you have enough days in Japan to do interregional travel.

Should we extend our stay in Tokyo, spend a night somewhere on our route to Kyoto...?
When you like to see a huge and populated metropolis, yes. Otherwise no. you can see a standard and average itinerary here and customize it in accordance with your preference.
http://www.japan-guide.com/e/e2400_tokyo_10.html