I think Kyoto is a must. Tokyo is also good because there are a lot of modern things and stores, but in Kyoto, you can enjoy both modern and old, Western and Eastern, at the same time. And you can do shopping in downtown. The best plan is to see famous temples and do shopping.

Yes.Kyoto,Tokyo,Osaka or Hiroshima,those cities are everthing famous sightseeing place.It's a typical traveling course in Japan. You can have an experience as much as you want to enjoy.However,as you know there are also international city which can see so many international people. It's completely depend on your interest. I don't knwo what do you want to see or to do. If you would like to feel like to drop in real Japanses cultuer,you would visit countryside. I recommend that Tohoku region,such as, Aomori,Iwate and Akita.There are not famouse,though you can see real Japan,in my opinon.even if we are Japanese,we can feel nostalgic. Moreover,Kyusyu region is nice too.But you should speak minimum Japanese.there are not many people can speak English.Also transportation is quite inconvenient..getting accommodation is hard too. I like to travel countryside.(^_^)v Have a good travel in Japan! I hope you'll be able to have the good experience and great memory in Japan.

Yes, Tokyo and Kyoto are great. Osaka is also very interesting. Hiroshima is important to visit. A great place is Lake Ashi, from where you have a wonderful view on Mount Fuji and can make a nice boat tour.