The first stop will easily be the UNESCO listed, Bryggen, the very first buildings in Bergen were alongside the harbour.
Nearby, the fish market can be fun.
For a view of the city, either take the Unriken643 Panoramic Tour or Fløibanen funicular.
There are several museum in the city, if the weather isn't great. But none of them are particularly spectacular. With the exception of Håkon’s Hall
By the time we got to Bergen, our last stop, we had seen a lot of fjords so we spent the day just walking around Bergen. If the weather is clear, I'd highly recommend the Floibanen funicular for a spectacular view over the city. We took the funicular up and walked back down, you can make your mind up about that at the top. No need to do a ship excursion, just go stand in line, it goes much quicker than you think
We also did a self guided walk that I found in Frommers, it was a nice way to get a look at the town
Like the other said, the Bryggen wharf and the funicular up the Fløyen mountain should be on the top of the list. Also closest to the cruise harbour you have the Kings hall, Håkonshallen with the castle grounds and the old fort Sverresborg just above it. If you are interested in classic music, you might enjoy an excursion to the composers home of Edvard Grieg. I also recommend a trip into the Tourist office for further tips depending on weather etc.
Greetings from Bergen!
For sure you'll not miss the Bryggen (not only the facade but also the complex). As the others said use the Floibanen funicular for the best view ever and what I wanna add is to take a walk in the Old City - steep and narrow streets behind Bryggen, see my little page - "The city with the best view" - Bergen by mirchica