Nowhere right now. All the European leagues (aside from Russia) are done for the season. Starts again in August. Right now your choices are MLS, Mexican League, or one of the South American leagues. Those last two will require the bar to have Univision or Gol!, which might be a problem on the Hill. MLS is sometimes on more common channels, but might be a hard thing to find tuned in on the Hill. It's just not a sports kind of place. Maybe the Roanoke, for Sounders games only?
During the European seasons, you might have better luck, but still the best places are all off the hill. Bear in mind that the games generally take place at uncomfortable hours in the morning; not everyone is up for a nice pint or two at 7 AM. But if you are, the George and Dragon in Fremont is a top spot, as is Fado downtown, and St. Andrews on Aurora near Green Lake. They'll usually replay the matches later in the evening, but be aware that if you already know the result from earlier and blab it out loud large angry men will ruin your night.
There are games being shown now on the screens of soccer-specific bars, such as the Copa Oro (CONCACAF Gold Cup, national teams from North America, Central America, and the Caribbean, which Mexico is utterly dominating at the moment). Many places will be showing the USA games. But the biggest game coming up is Sounders v. New York Red Bulls, Thursday at 4:30 PM.
Here are some pub schedule pages to bookmark:
http://www.georgeanddragonpub.com/ontelly.php
http://themarketarms.com/telly.htm
http://www.fadoirishpub.com/seattle/sports
http://www.theatlanticcrossing.com/ACevents.html
More here: http://www.prostamerika.com/seattle-soccer-bar-guide/