Silverwood Theme Park in Athol, ID, which the EB passes right by, is accessible by rental car either from Spokane or Sandpoint.
Good luck getting a rental car in either of those places when the EB rolls into town, though. You'd have to be really, really dedicated if you wanted to take Amtrak as part of a visit to Silverwood. I guess you could get a hotel room to spend a few hours until the rental car places opened.
I suppose if you wanted to arrive/depart in Spokane at a more practical hour you could take the Thruway bus from Seattle that arrives/departs Spokane during the afternoon. So technically that would be using Amtrak to get there, though not by train.