Is there a Turkish consulate or other office in or near Seattle where it's possible to get a tourist visa for Turkey?
You purchase it prior to going through immigrations in Turkey. It is $20USD for US citizens and you must have correct
change.
I went to Turkey in April and got my travel visa in the airport upon arrival. I was required to pay in euros and exact change was not necessary.
It's OK to pay in Euro: €15, or in Dollars: $20. Even if it's not required to have the exact amount I still recommend you do. I doubt the exchange rate for your change will be very advantageous.