If the point is to drive the most direct route to Seattle, Billings and Coeur d'Alene both good places?

It would be a lot more interesting drive to dip down to Yellowstone and the Grand Tetons or to the Sawtooth Mountains.

HTTY

Personally I would take MT 200 to connect with US 2 west. Spend the night in either Cut Bank or Browning which should take 8 hours. Take the GTTS road over Logan Pass in Glacier NP and then choose between Coeur d'Alene and Spokane.
This leaves the Yellowstone option available on the return trip.

Personally my aim would be to get through eastern Montana as quickly as possible. I gather you've previously visited South Dakota, so while I much prefer I-90 over I-94 (and wasn't especially knocked out by T. Roosevelt NP compared to Badlands and the Black Hills) I'd just try to shoot through Billings. I'd go either for Bozeman or, better but farther, Helena for that night. (Helena is IMO the most interesting major town in Montana - great history, architecture.) If you're meat eaters, make a point of dinner at the Land of Magic - http://www.landofmagicsteakhouse.com/ - in Logan (don't sneeze) partway between Bozeman and Butte.

You'll pick up an hour from the time change the next day, so Seattle is quite doable if a bit long. If you want an easy day, then Coeur d'Alene is quite attractive as an alternative. You might swing through Missoula en route - it's a very nice college town in magnificent countryside.

this is something you dont plan. you pull over and pick a passable place when the day is over.....its really that simple.

WOW!!! Cut Bank or Browning???? Why would anyone want to stop in either of those places when you can stop at Helena or Missoula.

On May 31 my wife and I got off the westbound Empire Builder in Cut Bank. We had our evening meal in a diner there and spent the night there before driving to the east side of the park on June 1. I agree if you want a more interesting place Helena would be a better choice. We enjoyed seeing the Museum of the Plains Indian in Browning before returning the rental car at the train station in Cut Bank. The train was 15 minutes late into Cut Bank but we got to Spokane 30 minutes early the next morning.
What I remember about my night in Missoula was that the air conditioning in the room was not working and the fan didn't help much either.

Helena is not on I-90, if you want to stay on the interstate.

I'd recommend Bozeman for a stop in MT. Once you get to Billings, it's two more hours to Bozeman, and five hours from Billings to Missoula. Missoula to Couer d'Alene is a little over two hours.