Location: Azabu-Juban station (Namboku line). 
Tel: 03.3444.4560
Address: 5-1-20 Hiroo, Shibuya-ku, Tokyo
Hours: Mon-Sat 11:00am-9:00pm ; Sun 11:00am-6:00pm
Website
Maps: Hirou, Azabu

How to get there: Use Exit 5a and turn left when you reach street level. Keep walking until you see a JOMO petrol (gas) station, a DoCoMo office, and several small side streets. After you pass the 3rd traffic light, it is the 2nd white building.

Apparently, Homeworks Hamburger cafe is the first gourment Hamburger Cafe in Tokyo, opened in 1985. 

They run two hamburger cafes, in Hirou and Azabu. They also do deliveries if your order is over 2,000 yen.