Federal Palace (Bundeshaus) Official Guided Tours Swiss parliament—dome views (free, book ahead).
Bear Pit (BärenPark) Free City symbol—bears along Aare river (free).
Zytglogge (Clock Tower) Official Tour Medieval clock—mechanical show (€12 guided).
Bern Cathedral (Münster) Official Gothic—tower climb views (€5).
Einstein House Official Where relativity theory born (€6).
Old Town (Altstadt) Free Stroll UNESCO medieval arcades—fountains (free).
Rosengarten Free Rose garden—city panorama (free).
Aare River Swim Free Famous summer float—locals swim downtown (free).
Paul Klee Center (Zentrum Paul Klee) Official Wave building—largest Klee collection (€20).
Bern Historical Museum / Einstein Museum Official History + relativity exhibits (€18 combo). Link