The Royal Park Tokyo Shiodome
Located just a stone's throw away from so/ra/si/o, The Royal Park Hotel Shiodome's 24F lobby bar presents a collection of beers, wines, and classic cocktails like the Margarita, Gimlet, and Martini during happy hour. They're all at half off the regular menu price, so enjoy the nice view as you relax with a drink. Stay for the live jazz as well.
You can also save even more by sitting at the bar instead of at a table -- this will shave off the 500 yen table charge.