Ridden through on the Glacier Express.
3 rail lines leading out of town. One up the Rhine valley to Disentis/Muster, Andermatt and points west. Another, the Albula line to St Moritz and points south to Italy. The other into Chur (8 to 9 minutes) and points east and north. So lots of day trip destinations within a hour or two. Chur is a nice town as well, worth exploring. Said (by the tourist board, probably) to be the oldest city in Switzerland. Flims/Laax is a ski town which I am sure has summer activities.

We overnighted in Chur last summer. Delightful place, with good hotels and restaurants and a walkable city centre.

1 day trip from Chur would for me be the Bernina Express over the Alps to Italy. It leaves Chur around 8:30 am and gets into Tirrano around 1:00, and you can go back the same day if you want. You could pay the extra to take the Bernina Express one way and go the other way on the regular SBB service over the same route but without the nice observation cars.

As the other two posters mentioned:

• Chur itself has a nice old town
• Glacier Express towards Zermatt
• Bernina Express towards St.Moritz and Italy
• Disentis has a big monastery
• Flims / Laax

Some additional points:

• It would be a shame to vacation in Domat/Ems without a hike/visit to the ruinaulta canyon near Flims
• Flims also has two nice little lakes in the forest
• Via mala gorge + St. Martin church in Zillis are worth a visit if those things interest you
• It would also be easy to see the Landwasser viaduct near Filisur
• St.Gallen, Appenzell and Zürich are all within 2 hours by train
• Somewhat more of a time investment but potentially interesting would be a journey with the restored steam train over the Furka pass.