We just got back from a cruise to Norway (on a different cruise line) and I just wanted to say that we found it super easy to explore on our own there. Very safe and friendly and everyone speaks English. My family hates being "herded around" and having to follow a schedule, so I always check out the other options. In Alesund we could take a taxi to the viewpoint with four people for a fraction of the cost of one excursion and had total control over when we came and left.
We also did a one day car rental at another stop and had complete freedom to explore the most beautiful scenery and visit a small stave church nearby. Again, the car rental plus half a tank of gas cost less than the least expensive organized excursion for one person. And when we drove past an adorable farm stand selling berries and jam we could just pull in and check it out like we could at home, no whipping past in a big bus.
At our last stop deep in the fjords I did a quick google search and booked a zodiac boat cruise with a company five minutes walk from the cruise dock. It turned out to be the same company the cruise company used, but instead of a big boat with 12 or more other people from the ship we got a smaller boat with only 3 other people. Again we paid less and had complete control over departure times.
Even if you don't usually do excursions on your own, I'd recommend checking out the options for Norway.