In addition to being genuinely cozy and a genuine tavern (no liquor), the Cozy Inn Tavern has a deck and a history -- it's been around since the early 30s. It's a comfortable neighborhood place with lots of wood and microwave pork rinds.
Closed 12/3/2013 while new building constructed, re-opened Aug 10, 2015 725 E Pine St, Seattle, WA 98122 - (206) 420-7493
Est. 1981 - Building constructed: 2015
Previous bars in this location: Mother's Tavern
Update: 2/27/2012: Since the night of this visit, Spring Hill upgraded their cocktail game to a fantastic degree, and then on Feb 8, 2012 changed their emphasis to Hawaiian and their name to Ma'Ono Fried Chicken and Whisky.
This relatively new place (6 mos. old) looks like a fine restaurant. But this list is about bars, and the bar here is an afterthought.