Is there a particular café that does anime coffee art?
Coffee art is commonly refered to as "Latte art" (ラテ・アート in japanese). By searching this term in japanese along with "anime" (アニメ) on the internet, you will be able to find many results (such as this blog where you will find many anime latte arts), and even many tutorials to make your own latte arts!

If you want to go see by yourself in a café, you can probably use this article as reference as it lists many recommended places in Japan where you can enjoy latte art. However, arts such as characters representations usually require lot of preparation/work/tries, so I would not expect too complex arts by going there in the first place.