Not sure if this is your thing, but this article was just published two day ago. I can't vouch for any of these places personally, as I rarely drink coffee myself.
https://tokyocheapo.com/food-and-drink/cafe/coffee-spot-hipster-tokyo-cafe-guide/
Awesome link - thank you!
For Shibuya the coffee isn't blow-you-away awesome but just in terms of cafes I'm a big fan of Lil Rire -
http://lilrire.com/
The atmosphere is great and the food is awesome (if slightly pricey). Its American diner food by way of Japanese hipsters and if you dig that kind of fare its SOLID.
The fried chicken and biscuits is awesome and their Popeye Rice (spinach rice with pork and egg) is great too.
Its tucked away about 3 minutes behind Bunkamura so its usually not crazy crowded either.
Freeman Cafe in Shibuya is also pretty spacious and has some pretty decent coffee -
http://tabelog.com/en/tokyo/A1303/A130301/13124332/
For killer coffee I really like Be A Good Neighbor in Harajuku
http://goodcoffee.me/coffeeshop/be-a-good-neighbor/
Its just a takeaway kind of place - there's no seating - but the coffee is stellar and the prices are reasonable.
There are a lot of good places around Shimokita too but I really like the coffee at Bookends
http://www.live-coffee.com/product_store/store/shop/01/index.html
Its tasty and SUPER cheap.
Swinging totally the other direction I'm also a big proponent of Seibu in Shinjuku if I'm going to be having a meeting:
http://tabelog.com/en/tokyo/A1304/A130401/13048352/
Its very much a Showa style cafe and some of the prices are a little wonky (a small cup of coffee will set you back about 600 yen) but you aren't paying for the drink - you're paying for the ability to have a comfy seat 2 minutes walk from Shinjuku station and literally stay there as long as you want. You can also grab a meal or a giant parfait for about 1000 yen, which is a bit more cost effective. Highly recommended if you need to get some work done!
