Fantastic city – one of those where the first thing we did on getting home was give serious consideration to relocating there.
I remember the final approach to the airport above the fjords being spectacular, so a daytime flight might be best. Plenty to do for a long weekend, if the weather is good a trip up the funicular and hike around the top is worthwhile, as is a fjord cruise, which aren’t terribly expensive. If the weather is bad (it will be) then there’s a lot to see around the Bryggen/harbour area without breaking the bank.
We stayed in a self catering apartment called Gullakassen (?) which was very reasonably priced by Norwegian standards, run by some lovely people who were very accommodating when we kept asking to stay a few days longer.
It did rain a lot!