Max S.
Yelp
The perfect neighborhood coffee shop with free wifi and delicious coffee at a great price. This is really one of those spots that I would love to become a local at, because of their attention to detail, emphasis on quality of each cup rather than quantity of sales, the friendliness of the baristas there, and the excellent pricing.
They have delicious baked goods as well, though they're a bit pricy. Fuglen also sells quality cocktails at night, so if you're looking for a hangout spot with both coffee/alcohol, Fuglen is your place. And while the Japanese tend to understand the term "cocktail" to be what America calls cheap mixed drinks, Fuglen's cocktails are the real deal.
If you're looking for coffee in Shibuya, avoid a $6 mediocre cup and come to Tomigaya/Kamiyamacho where Fuglen is located - a more quiet, artist's alley / hipster neighborhood.
I also have to say, this is the best "third place" I've found in Tokyo yet, and I've explored a ton of cafes. The decor and atmosphere are great, locals come and go, and the wifi doesn't cut out each hour - I could spend hours and hours here, except for the lack of power plugs.