Bear Pond: Kind of “famous” I think, coffee-focused to the point of arrogance, but Shimokitazawa is an awesome neighbourhood worth visiting anyway (and I bet there are other good cafes around now too).
Fuglen: Nicely designed Scandi-style place, very relaxed.
Little Nap (close to Fuglen): Super cool tiny place, Americana-themed(!) if I remember correctly.
Be A Good Neighbour: on the other side of the park in a quiet neighbourhood. Lovely bright corner space with massive windows.
Streamer Coffee Company: there are actually a few of these (here’s another) I think, very good coffee. One of these (I can’t recall which, I think it might be in Harajuku) is actually a giant vertical stack of shipping containers!
On The Corner: This is a little Bear Pond Espresso outpost in the front of a diner. The diner is very nicely designed and a good spot for lunch with your coffee.
The Coffeeshop is a tiny hole-in-the-wall and did some great coffee but IIRC it wasn't close to anything super interesting. Worth it if you're wandering in or through that area tho.
Cafe Kitsune is good if you're in the Omotesando area: It's actually just a little cafe inside a Kitsune fashion shop. They used to serve Omotesando Coffee, too (this is a world-famous place in an old japanese building that recently shut down 😿)
Saturdays Surf NYC is a cool surf shop serving coffee with a massive back balcony which would be nice on a sunny day. Also, designed in true minimal Japanese style, totally not what you'd expect e.g. from surf shops in .au
Nozy Coffee: This is also a bit out of the way IIRC but they're super coffee focused, serve a great cup.
Cafe Obscura. I just loved the design here: unassuming, built entirely of raw concrete, comfy seating.