This place is located at the top of the island so you do need to hike up a hill to reach but it's absolutely worth it.
Most of the cats on the island gather here throughout the day.

The cafe food is simple but very cute and they also sell very cute merchandise.
Just beware, they finish serving food very early at 14:30 and close by 15:00.

About:

Tashirojima Nyanko Kyowakoku Shimanoeki is a cat lover's dream come true, located on Cat Island in Japan. This cozy rest house is filled with dozens of friendly felines lounging around, ready to be petted and cuddled. Visitors can enjoy snacks made from local ingredients while surrounded by adorable cats who are more than happy to receive some love and attention.