Good places to stay along the Bernina Express route?

Poschiavo. Stayed there a long time ago. Little Italian speaking town on the Italian side of the Bernina pass, but still in Switzerland. The station is on the edge of town, easy walk to hotels.
Click here for picture of town square.
Click here for a topographical map of the area (you can pan and zoom it).
Click here for local tourist information.

If you want a town, there are lots of places in Pontresina. Hotel Steinbock is very moderately priced, and gets good reviews.

But we prefer the little mountain inns, which is what you will find at those railway stops where there is no town. These are part of the charm of Switzerland. Most have access to good hiking, and provide nice meals.

Like you we will be traveling from Zurich to Italy and have several days to spend along the way. I specifically booked this route as we have spent a lot of time in Switzerland but have never yet made it to the Engadine. We want to spend two nights in one place along the route--- two nights so we will have a full day for hiking, and also because most of the hotels offer a free local transport pass ( trains and lifts) with a two-night stay.

Our choice will be the Gastehaus Bernina, an historic mountain inn a bit south of Pontresina, with its own railway stop. We prefer this to a place in town where we would have a loooong walk, or taxi or bus ride, from rail station to hotel.

http://www.berninahaus.ch/

There are others, in more remote locations. Some are quite famous, and all are much-loved by the Swiss. Depending how much time you have,one of these might suit you.

Thanks for the thoughtful replies -- Poschiavo and Pontresina look like they would be perfect for the second leg of our trip through Switzerland.

Are there any recommendations for a village to stay in the first night between Chur and St. Moritz?

Villages like Thusis, Tiefencastel, and Filisur seem like a good distance from Zurich to make our first stop.

Take a look at Berguen.
Edit- It has the Albula Railway Museum with a toy train layout of the Albula rail line so you get a good idea of the Bernina Express line layout with its helical tunnels. www.myswitzerland.com calls the town "unspoilt". Maybe they mean Lauterbrunnen has been "spoilt". There are few hotels there including the old Kurhaus. Lots of hiking routes.

Bergün looks like a great place to stay but unfortunately is all booked up the night we would stay there.

Now I'm looking at either Thusis or Filisur for a place to stay. Any thoughts on which might be better?

I only know that Filisur is below the train station, so its a bit of a hike from town up to the station. I know this is the antitheses of the cute Swiss village, but Davos is just a 30 minute train ride away from Filisur. But hey, they have a casino!