Unfortunately that's what things cost during cruise season. Many cruise pax departing from Vancouver find that airfares into SEA are considerably cheaper than into YVR, but then they discover that the surface logistics - SEA to hotel, hotel to train, train fare, then train to dock in Vancouver, all can easily erase the cost advantage. The good news is that the train ride is quite scenic, and won't be affected (aside from probable overbooking) by the highway troubles with I-5 due to the bridge collapse.
Pretty much any downtown hotel will be within a $10 cab ride of the King Street (Amtrak) station. Hotels near Seattle Center/Space Needle will be less convenient, but not out of the question.
I'd look at a couple of properties that fall under the radar sometime. The
Silver Cloud Stadium hotel is across the street from Safeco Field (Mariners) and have a local van that I believe will take you to the station (which is around 4 long blocks from the hotel if you want to walk.) Silver Cloud's
Broadway branch is another possibility.
The downtown
Courtyard by Marriott is a good property located at the south end of downtown, walkable (maybe) from the station. The Doubletree
Arctic Club is in a wonderfully renovated historic office building nearby. Both are very walkable from the Pioneer Square light rail station (service from the airport) so you could save some money the night before by taking the train from the airport in the first place.
Otherwise, of course there's always Priceline and Hotwire.