Bern is the capital that doesn't behave like one. Switzerland doesn't officially have a capital at all: Bern is the federal city, the seat of government, chosen in 1848 ahead of Zurich and Lucerne. The old town sits on a narrow peninsula in a loop of the Aare, founded in 1191 and rebuilt in sandstone after a fire in 1405, which is also why its streets are lined with arcades. It has been a UNESCO World Heritage Site since 1983, and the center looks so coherent that it feels staged. It isn't. People live and shop under those arches.
Three days is the right length because the old town is compact: you can walk the length of it in well under an hour, so the whole core fits into one day. The second day collects what sits just outside it, and the third goes out of town, because cheese country and a second medieval city are within an hour and a half by train.
Day one is the old town, from the Zytglogge clock tower to the bears. Day two is Klee, Parliament and sunset on the Gurten. Day three is a day trip to Gruyères and Fribourg. Start on a Tuesday if you can: Monday closes Zentrum Paul Klee and most museums, Parliament tours run Tuesday to Saturday, and shops are shut on Sunday. Our Switzerland page has the bigger picture, and Bern sits well between 5 days in Zurich and 5 days in Interlaken.