Formerly a hostel for the homeless and before that a home for maritime workers, this 29 room hotel opened for business in 1999 to become the first in what is now a small but international (US, UK and Panama) chain of Ace Hotels. Located in the once run-down but now trendy Belltown district, Ace combines ultra-cool design with real affordability, just so long as you're happy to walk down the hall to the "private-upon-entry" bathrooms / showers. If you prefer your own en-suite facilities, there are a limited number of deluxe rooms with bathrooms.
If you go:
There is no in-house restaurant but the the Cyclops cafe and lounge is based in the same building and there are plenty of other restaurants and bars throughout Belltown and the Pike Place Market is only a few minutes walk away.
Links:

2423 First Avenue
Seattle, Washington 98121 USA
Phone Numbers:
+1 (206) 448-4721