Piz Corvatsch
A cable car (2 sections) takes you up to P. Corvatsch, preferrably on a sunny day. The views from the summit (3303 m) are breathtaking. Depending on the weather you can see the Monte Rosa massif above Zermatt, the Mischabel mountains above Saas Fee, the Bernese Alps and many more. Just for fun do some steps on the glacier!
I highly recommend to get of the cable car on your way down at the middle station Murtel (2701 m) and add a hike via Fuorcla Surlej (2755 m, 45 min.) to the Roseg valley. The views of P. Bernina (4049 m), P. Roseg (3963 m) and others with their glaciers are stunning. There are three hiking paths which lead you from Fuorcla Surlej down to Hotel Roseggletscher (1999 m). The shortest one will take you about 2:30 hours, the longest one (via Coaz hut) about 5 hours.
From Hotel Roseggletscher to Pontresina railway station take the scheduled horse drawn carriage, rent a bike or hike (1:30 hours).

St. Moritz (video)
Mountain railway (video)
snowcapped mountains in summer time
St Moritz Lakeside