A hidden treasure of the Tokyo happy hour scene is Shiodome's so/ra/si/o. Located on the 46th floor of advertising agency Dentsu's headquarters, this French restaurant features a sweeping view of the Tokyo Bay area near Rainbow Bridge. In addition to the magical dusk/nighttime scenery, the happy hour in the bar area is pretty amazing: 50% off all drinks in the bar. Beer, wine, champagne, whisky, cocktails--whether or not it's shown on the drink menu--it's 50% off. Since cocktails start at around 1200 yen here during normal hours, it's a significant savings. I don't know of any other "sky bars" providing a happy hour this happy.
The happy hour runs from 5-7PM everyday, even weekends, and there's no seating charge. It's only applicable in the bar area, which seats around 12 people at most, so be sure to arrive early. Given the location, so/ra/si/o is also a popular location for wedding receptions, thus I recommend calling in advance to make sure they will be open when you plan on going.