newtown,
I suggest you conduct a search of your own. I don't have enough info to really help more than I have. You haven't provided your exact dates, so I am not sure that the results I found and screenshot yesterday (and confirmed they are still available as of now) are accurate. If indeed your dates are June 6 - June 12 I don't know what time you are arriving/leaving...
To answer your question, No- the $120/week car is at an Enterprise location at 11717 Lake City Way NE Seattle, WA (this is on the screenshot). You can enter this address in maps.google.com click directions enter the airport and select public transport. Find out what time you are leaving... and it will show you bus routes. My quick search showed about 1:20 and $5, with one transfer in Chinatown.
Enterprise will come and pick you up. But not from the airport. You will need to get out of the airport. You will also need to set up a pickup by phone, in advance. Or, just take the bus, it will get you there in basically the same amount of time. And looks like it will drop you off very close.
You can also Uber there, but to this particular address, it is a good distance and would cost accordingly.
Again, your luck may vary...
Brian