Personally I would park at the Davenport Hotel parking garage rather than the Amtrak station. The garage is at First and post just a few blocks from the station. Self parking is $17 per day.
I think you could park for a whole lot less than that at the airport or Amtrak itself?
Unless you really need to park your car inside, that is. Smash and grab is not a huge concern in Spokane, although admittedly, I don't have that nice of a car.
As I stated before, I would not park at the Amtrak station especially for that many days. There are a lot of vehicle prowling incidents in Spokane. I would want to park inside due to weather and also for security. Sure, you can park at the airport but then you need to ge to and from the airport to the Amtrak station.