KingslandBarge Never been to Flåm, but I used to live in Bergen. It's a really nice city in my opinion, hopefully you're lucky with the weather.
Bergen is surrounded by 7 small mountains. There's a trail that visits each of these. Not sure what kind of shape you're in, but if you are it's called 7-fjellsturen (7-Mountain Tour). If not, there are shorter versions of the trail where you don't visit each of them, 4-fjellsturen and 3-fjellsturen.
And if you want to not do everything in one day, you could also do them individually. Fløyen is the most casual, probably just an hour to get to the top and with a nice view of the city and a restaurant at the top.
Ulriken is one of the others, and has a cable car to get to the top as well if you don't want to walk. There's a restaurant at the top called Skyskraperen Restaurant with panorama windows overlooking the surrounding landscape. Never been there myself, but it's become pretty popular. Takes less than three hours to walk to the top I think.
As for restaurants, I lived there as a student with limited funds so didn't try that many of them. Not sure if you're into fine dining or not (I've never been one to spend £150 per person for a dinner) but there are two Michelin restaurants in the city called Moon and Lysverket. I've also heard good things about Bare Restaurant and Restaurant 1877, but these are all 'exclusive' choices. On the other side of the scale you could go by Trekroneren hot dog stand for a reindeer hot dog.
Bryggeloftet is also supposed to be good for Norwegian cuisine. Not as expensive as the first ones I mentioned, but not cheap either. However the Norwegian Krone is worth less compared to GBP than ever before, so that should help you.
People who live in Bergen are extremely proud of their city so they'd probably be happy to recommend you something if you asked a random person. If you're there in the summer most of the people you meet will be from there (or tourists, I guess). If you're there other than the summer I wouldn't ask young people since they're probably students and won't be able to help you that much.
Like I said, I've never been to Flåm, but I've only heard good things. It's famous for it's zipline (1,4 km long) and obviously nature in general.
Stegastein Viewpoint
Ægir Bryggeripub (food and beer)
Nærøyfjorden (either by ferry or kayak)
https://www.alltrails.com/norway/vestland/flam