6th by Oriental Hotel
Conveniently situated just across the street from Yurakucho's Bic Camera is 6th by Oriental Hotel. While the hotel itself is in Kobe, the restaurant here has an extensive food menu. There are a wide variety of seating options: indoors, on the terrace, at the bar, or in the cigar lounge. Since the main dining can get noisy, if you are only here for drinks, I recommend sitting in the bar or lounge (pictured).
No matter where you sit though you can enjoy the daily happy hour from 5 to 7:30PM, where a selection of drinks drops to 500 yen each. Of course there are standard options like beer, sparkling wine, and highballs. For the heavier drinker, there is always at least one of their signature martinis available for happy hour. Those will ordinarily set you back around 1200 yen, so a discount to 500 yen is 60% off.
Due to its location, this restaurant tends to fill up quickly regardless of the day of the week. Arrive early to ensure you get a seat!