The Engadine is Alpine Skiiers' heaven. All in all about 350 km runs are prepared. It sounds huge, but the resort is divided into some separated areas.
The most frequented and probably most famous is Corviglia/Piz Nair above St. Moritz. Altitude 1800 - 3025 m. The lifts are up to date (chair lifts/gondolas/cable cars only). In 2003 the Alpine Skiing Championships took place here. Access from St. Moritz Suvretta (chair lift), St. Moritz Bad (Signal cable car), St. Moritz Dorf (Corviglia funicular) and Celerina (gondola). Free parking at Suvretta, Signal and Celerina, frequent Ski bus service to Signal, St. Moritz Dorf and Celerina. Most of the slopes are sunny and well manageable for intermediates. Some easy runs around Corviglia and some difficult runs at Fuorcla Grischa and Trais Fluors. Snow conditions are (almost) always perfect. A secret spot: the chair lift Lake della Pesch to Fuorcla Grischa (intermediate). Plenty of restaurants, high quality, but most expensive in the Engadine's skiing areas. I recommend the Corviglia self service restaurant, or still better the bistro with daily offers of outstanding quality for about 18 Sfr. Excellent food and the best hot chocolate ever at "Chamanna" on Munt da San Murezzan (operated by five star hotel Suvretta).
My favourite area is Corvatsch/Furtschellas above Silvaplana-Surlej and Sils. Altitude 1820 - 3303 m. Absolutely snow reliable. The perfect area for spring skiing. It is more challenging than Corviglia, but offers intermediate runs as well. The upper section between Murtel and the top of Piz Corvatsch is really outstanding - the runs lead across a glacier, away from the lifts or cable cars - pure nature and you. These runs are never crowded, because the capacity of the cable car to the top is limited. So expect lines at Murtel :-( However, don't miss a trip to the Furtschellas area, which is really remote and fine. Most favourite run is the standard run from Murtel down to Alp Surlej and further to Surlej. Another unique run is the run down to St. Moritz via Hahnensee restaurant, again away from lifts. Good and cheaper restaurants everywhere (Alpetta is cosy, Fuorcla Surlej is charming, excellent wood oven Pizza at Murtel). Fine Apres ski at Alp Surlej till 8 pm, every Friday night skiing till 02 am with party at Murtel!! Ski buses operate between the Engadine villages and the cable car stations.
A third big area is Diavolezza/Lagalb. It is somewhat off the beaten path, some 20 km from Pontresina toward Bernina Pass. Altitude 2100 - 3005 m. Very snow reliable!Diavolezza is sunny and mild, but offers stunning views of the glaciers and peaks in the Bernina massif. The upper part of the runs leads across a glacier. Intermediate and challenging runs are available. A special run is the route down to Pers and Morteratsch glacier and further to inn Morteratsch at the train stop. Marked, but not groomed. For experienced skiiers only! Night skiing on the standard run with party at the hut when full moon. Lagalb is very challenging, is served by a cable car and almost always has great snow. Absolutely off the beaten path, never crowded. A ski bus runs between both Diavolezza and Lagalb. Skibus and railway from the Engadine villages to both stations.
There are some other small areas in addition, worth to try out for a half day or for some relaxed skiing: Muottas Muragl, Zuoz and Maloja e.g.
However, skiing in the Engadine is always great, a combination of adventure, fun, fascinating landscape and great food.
Rental stations everywhere in the villages. On Corviglia as well. I use to bring my own to reduce costs. Ski Pass is about 300 Sfr. for 6 days - not even cheap, but public transportation and the indoor pools in both St. Moritz and Pontresina are included.