Best locations for honeymoon?

Hi, I am planning a honeymoon vacation with my wife to Japan, but I am so unsure about which prefecture and city to stay at. (Edit) We plan on going late May / early June (a couple years in the futute) in hopes avoid huge tourist crowds, and to perhaps experience the cherry blossoms. I absolutely adore japanese culture, food, architecture, etc. We are not the typical "city" people. I have tried researching myself watching youtube videos and using Japan's official travelguide map, but I feel lost. There is so much my wife and I wish to experience. I hope I can give a list of our interests and what we would like to visit, and get some advice. Our budget is mid- to high end areas / hotels.

Thanks in advance.

Nature. We love nature. The more green, the better.

Animals. We both grew up with animals (dogs, cats, cows, ect.), and would love to be able to visit exhibits (with good animal treatment), or simular (my wife is obsessed with Ao Island and cat cafées).

Transport. It is a pluss to be close to nature reserves or other attractions, but not a must as long as there are good options for public transport.

Food. Self explanotory. (Edit) Perferably vegan options.

Botanical gardens. Nature.

Studio Ghibli attractions. We are huge lovers of the studio ghibli movies. Visiting stores, museums or a live orchestra would be awesome.

Nara Park. We wish to visit those bowing deers.

Ao Island. Wifey is obsessed with the imfamous Cat Island.

Thanks.