Shanghai to Japan

We (from Istanbul) plan to visit Shanghai for two weeks, but also want to fly to Japan from Shanghai for a few days and return back. Can you fly to Japan and back from China easily, or either country is hostile towards travellers from the other one? We will be in Japan between March 29th and April 3rd, what type of a trip would you recommend? Anything to focus on? I think it is Sakura season, we want to visit Kyoto and Mt.Fuji (from afar) as well.

by Gordias