I've never been to Basel or Zurich so I can't comment on that, but I have been to Amsterdam, in every season, and love it dearly. Most recently, we visited in early December of 2019 for four nights - part of a longer trip spent visiting friends and Christmas markets in Vienna, Münster, Essen and Cologne. We loved it so much, we plan to return next Christmas - if possible.
Amsterdam doesn't have any Christmas markets like you'd see in Germany or Vienna, but it is lovely nonetheless. And yes, the Anne Frank House is an absolute must. I also recommend visiting the Rijksmuseum - the Night Watch was just recently restored and is marvelous. Two things I love most about Amsterdam: (1) it's small; therefore, easily enjoyed via walking, tram and canal boat, and (2) the canals & canal houses make the city - in my opinion - one of the prettiest in Europe. We especially love the Jordaan district and have stayed there on every visit (four and counting). In December 2019, most streets had Christmas lights and decorations - nothing over the top, but tasteful and pretty. The Saturday morning market located at the Noorderkerk was delightfully festive; a person with a Dutch street organ was playing Christmas songs for small tips, and vendors were selling Christmas trees, garlands and wreaths - in addition to the normal offerings of cheese, fruits, vegetables, bread and baked goods.
One thing too keep in mind is that it gets dark very early, but the twinkle lights reflecting on the canals makes it that much more festive and atmospheric. Each evening, we'd loved stopping into our favorite brown cafe to soak up the cozy atmosphere with a beer or warm beverage. There are some wonderfully unique, small independent stores in the "Nine Streets" neighborhood (part of the Jordaan) where we did a bit of Christmas shopping, and a lot of window shopping. If you have young children, grandchildren or are a child at heart: don't miss The Mouse Mansion Shop & Studio located at Eerste Tuindwarsstraat 1HS, 1015 RT Amsterdam (plug that address into Google Maps and save the location). This delightful shop is an absolute one-of-a-kind gem for children of all ages. A few of their books are in English and made wonderful gifts for our young nieces and nephews.
With four days, you could easily do a day trip to either Haarlem and/or Delft - both are are just a short train ride away and easily navigated on foot from the train station.
Hope this helps.