In early October we plan on traveling from Zermatt to Ste Moritz area via the Glacier Express and onto Rome via the Bernina Express through Lugano. We are thinking of staying a day or so in the area at the end of the Glacier Express before proceeding onto Lugano. Would appreciate thoughts on sights to see and places to stay.
St Moritz is an old money glitzy kind of place (like Zermatt) so if you want to stay somewhere close but less glamorous, Samedan and Pontresina are nearby. Local trains will take you back and forth or it is possible to hike back and forth to St Moritz. Take the local trains down valley to some of the untouristed smaller towns and see really peaceful Swiss life. You will see some signs including Romansch in the area, which is kind of interesting. Rick Steves does cover this area (Graubunden) in his book, with recommendations.
I will endorse Stan's suggestion of staying in Samedan or Pontresina, unless you particularly want the "old world resort" feel of St. Moritz. These towns are all connected by train ( a few minutes apart) and hiking trails if you are interested. Lots of them.
We were there in late September and chose to spend two nights in Samedan---I found a reasonably priced garni which was perfect. It was an easy walk from train station and to a trailhead for hiking. The town is quite small. Pontresina is larger and has more to offer in the way of hotels, restaurants, and shops.
The Bernina Express is now my favorite train ride in Switzerland---stunning scenery. We rode a regional train rather than the designated scenic train.
You might consider taking it only as far as Tirano and skipping the bus transfer from Tirano to Lugano, unless you have a particular desire to see Lugano. From Tirano you can continue by train into Italy and reach Varenna on Lake Como in 1.5 hours. We did an overnight there before continuing to Milan (1 hour from Varenna) and on to Venice right away. You could get to Rome just as easily.
As you plan on travelling in early October, hopefully the Bus connection from Tirano to Lugano will be operating. You'll need to verify that.
If you're travelling onto Rome the same day, it would be far easier and quicker to just take the Regionale (TreNord) from Tirano to Milano Centrale, and then connect with the high speed Freccia or Italo trains there for the last segment to Rome. Don't forget to validate your tickets prior to boarding any Regionale trains!