In 2010 when I was in Switzerland for one year we did the exact same trip: Bern first and then Thun - a small city located just a bit south and just a bit east to Bern - right at the foothill of the Alps. Thun is a pretty little place and we decided to treat it as a starter to even more beautiful mountain resorts that we want to see this winter. Also, since I didn't feel that well health-wise, we decided to go to Thun which was the closest to our location.
The atmosphere of the city was way more hectic than at Bern. We first went by the city promenade - full of young people, Christmas emblems and crazy window displays. Then we headed to a boulevard stretching along the Thuner See (Thun Lake). A look on the Alps felt like a foreword to the views that we are going to see when we visit villages even more to east and south.
On our way back we went through an old city alley that was heading to the castle. Unfortunately, we didn't make it to the top. We decided to return to car because I was feeling more and more ill. Better to save my health for later - in the end, I already saw the castle in 2010 (photos from 2010 below).
And here is a view from the castle hill in 2010 (just four years ago but seems like an eternity now):