Two days is about right: the wooden wharf and the museums when it rains, one of the two mountain lifts when it clears.
Bryggen
The row of wooden Hanseatic trading houses on the east side of Vågen, on the UNESCO World Heritage list. The passages and galleries behind the front row are open and free to walk; early morning is the only time they are quiet.
Bryggens Museum
Built directly over the medieval excavation behind Bryggen at Dreggsallmenningen 3, so the foundations of the city's oldest buildings are part of the exhibition, along with runic sticks and imported ceramics. Daily 10:00–17:00; 170 kr adults, free under 18.
Fløibanen funicular
Runs from Vetrlidsallmenningen 23A, a few minutes' walk from the fish market, up Mount Fløyen; 07:30–00:00 daily, ticket office 08:30–21:00. Walking back down through the woods is free and takes under an hour.
KODE Art Museums
Four art museums in the city centre — Lysverket, Rasmus Meyer, Stenersen and Permanenten — run as one institution, plus three composers' homes outside town including Grieg's Troldhaugen. Summer hours at Rasmus Meyer are Tue–Fri 10:00–18:00, weekends 10:00–16:00.
Ulriken643 cable car
Cable car to the top of Bergen's highest mountain at 643 m, with a restaurant, café and marked trails at the top; 255 kr one way for adults, 120 kr for children 4–16. Daily 09:00–23:00 April–September; closed Mondays and shorter hours the rest of the year.