FAB cafe
FAB might be a little farther away from Shibuya station than other cafes, but it’s definitely worth the walk. Treat yourself to their signature ‘marshmallow latte’, the cutest drink I’ve ever come across. 
Photo courtesy of youfuku00nikki.blog135.fc2.com
Mobile working place
If you want to get creative this is the perfect place. With their 3D-printer they can print your design of choice on any item of choice, of just print a totally new design in thin air! I’ve seen people walk away with slick designs on skateboards and laptops, or 3D renditions of any design they conjured up. Perfect to pimp up your business cards! It can get crowded, but the facilities are good and the tables and chairs comfortable. And of course, a fast Wi-Fi connection is available for those who can still concentrate on work amidst all the 3D excitement.
Mini-me
A design on a laptop? Your design imprinted in your favorite pen? All cool, but if you really want something unique you can have yourself (!) printed as a tiny figurine. How awesome is that! You need some 4 to 5 days, since it's quite an intricate process. After making an appointment (making a tiny self is apparently popular), you are laser-measured. All very sci-fi. Then, they start the printing and you can pick up your own mini-me in 3-4 days!
Website: http://tokyo.fabcafe.com/en/
Address: 1-22-7 Dogenzaka, Shibuya ku, Tokyo
Tel: +81 (0) 3-6416-9190
Hours: daily 10:00-21:00, weekends 11:00-21:00