There is no free parking but there is a couple of parking garages across the street that usually always has parking. And there is a paid parking lot within a five min walk. The prices are all about the same. $17-18 for 10 hours. The parking garage directly across the street does not take MasterCard but takes Visa. Butler parking garage which takes Visa and MasterCard but there is only parking like 6 or 7 floors up. If you plan on needing parking all the time there is a app you can download Quick Pay and you don't have to deal with the machine. Also, if you plan on needing parking on a regular basis there is parking garages with 10 min walk that are like $150-200 a month for a parking pass. If you don't want to deal with parking you can take the Lightrail or the Sounder Train they both drop you off within a couple of minutes from the Smith Tower.
We kept our car at the hotel and walked. You can also use Lyft
Parking in Seattle is pretty expensive just an FYI
You might find some street parking. If not, plenty of lots around. Avoid on game days as there will he a surcharge for parking.
The lightrail Pioneer Square stop is right at Smith Tower. Also a short walk from downtown
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