There's some wonderful hiking around Bergen itself, given that the city is surrounded by seven peaks. The most popular mountain areas are Mt Fløyen and Mt Ulriken. There is a funicular which runs to the top of Mt Fløyen, if you don't want to hike uphill.

A short tram ride out of central Bergen, there's the Fantoft Stave Church, as well as Troldhaugen, Norwegian composer Edvard Grieg's home. The estate overlooks a fjord, so it's a really lovely spot to visit even if you're not into classical music. (Not sure if these count as "boring museums" )

If you're looking to do a bit of food and beer "sightseeing" while in Bergen, here are a few of my favorite spots: Søstrene Hagelin (traditional Bergen style fast food); Pingvinen; Spisekroken; Bjellands kjøkken (traditional restaurant run by an 80-something y.o. lady, who is a well-respected local chef and cookbook writer).

Apart from that, well, I think by getting out of Bergen and covering Flåm etc - you're already covering a lot of the natural highlights of the region. The Flåm railway is great fun. I did those small towns/fjords as part of the Norway in a Nutshell trip out of Bergen and didn't stay in each area for long, so hopefully someone else chimes in with additional tips on the areas outside Bergen!