Suggestions on kyoto mainly

I will be spending 14 days in japan (minus air flight time) and I will be arriving in Hanade Airport.
I will be going tokyo for 4 days first, staying at shinjuku area.
Followed by going to kyoto for another 4 days.
Back to Japan for the remaining 6 days.

I need suggestions on
-Where to shop around shinjuku
-What transport would be the best from tokyo to kyoto
-Where am i able to stay in a local homestay with the traditional style
-What are some of the shrine or attraction i should explore in kyoto

-Where to shop around shinjuku

Perhaps Miraina Tower beside the station? It's a new development.


-What transport would be the best from tokyo to kyoto

Japan's world famous Shinkansen.


-Where am i able to stay in a local homestay with the traditional style

Many places. Try a hotel booking website. Plenty of photographs and user reviews.


-What are some of the shrine or attraction i should explore in kyoto

Look no further http://www.japan-guide.com/e/e2158.html#section_spot_list


BTW, Kyoto is still in Japan.

Where to shop in Shinjuku? What do you want to buy?

Shops are everywhere, you cannot take 5 steps without finding a store. In fact, the whole Shinjuku Station Building is like a giant mall.