These are my personal favorite ski destinations, with nice resorts and reasonably easy slopes in Europe:
A.If you want to ski on the Mont Blanc: Chamonix (FR) or Courmayeur (IT). Nice resorts, reasonably updated lifts. Nice multicultural/younger crowds. Excellent food at reasonable prices. The offer of apartments, AirBNB and Hotel rooms is very large, so even in peak season you can find something for almost any budget. Downsides: cars everywhere during peak season! It’s a mess to move aroundunless you walk (but the villages are pretty large so everybody uses the car).
B.If you want to ski on the Matterhorn / Mount Cervin / Cervino: Zermatt (CH) or Cervinia (IT). The slopes are fantastic and the domineering view of the Matterhorn is absolutely intoxicating (of the two sides, the Swiss one is probably more beautiful). The slopes are well groomed and the lifts have mostly been renovated in the last 10 years. Ski teachers are multilingual and very kind (but cost like a London finance lawyer!). Zermatt is completely car-free and you can reach it very easily by train from Zurich or Milan: fantastic. Downsides: Peak season is after January 6th (Orthodox Xmas) because of the inflow of wealthy Russian visitors (in January prices are very high). Also: there is basically no nightlife (at night the silence and gentle light system throughout the city will make it look like a fairytale Alpine village) and the people skiing there are mostly the age of your parents.
C.If you want to ski on the Dolomites: Cortina d’Ampezzo (IT). Excellent slopes with very nice views over the Dolomites. Food is good and the village is beautiful and well-maintained. Hotels are a bit old but with charme. The crowd is mostly Italian, with the occasional foreigner. Downsides: Cortina is very expensive (not just for Italian standards: I compared the prices in January and they are generally on par or more expensive even than Zermatt)and it can only be reached by car or coach bus. Also, you will most likely need a car to move around as the city is pretty wide and some of the best slopes (San Cassiano, Alta Badia, etc.) are only reachable by car. The closest slopes are Faloria (walking distance from the city center) and Socrepes (take the n. 3 bus). January/February is peak season, so prices are normally driven up too.