Public parking --- metered --- in downtown Seattle is typically $5-7 an hour for no longer than two hours (fours hours in outlying areas). In the last few years, the City of Seattle has increasingly looked to its metered parking, and the fines for their violations, as a source of income & has correspondingly increased its enforcement. You might be able to find extended private parking in downtown Seattle, but, because parking downtown is scarce, I would expect it to be expensive. A day's parking in private lots downtown is typically $25-50. In my limited experience, the Seattle Library has the least (or is close to the least) expensive all-day parking downtown.
A longtime Seattle resident (on Queen Anne) who eventually moved across Lake Washington to the eastside.
Alta & Richard, Olympia, WA --- WBCCI 8873
"Aurum": 2018 Ram/Cummins 3500
"Argentum": 2016 AS FC 27 FB
"BigDog": M Harlequin Great Dane, 150 lb
WL7Z --- NAUI --- WSBA