I play Neko Atsume, a "cat collecting" app. It has rooms and gardens, cat furniture and toys and food, and of course, cats. Certain furniture or toys attract certain special cats. The graphics are very good.

It's not a complicated app, but it has gotten some good reviews. Oddly, one of the reasons I like it is that the instructions are all in Japanese, so you have to do detective work to figure out how it works. I think only people who seriously like cats would enjoy this app.