Holland America cruise to Iceland

I've never been on a cruise but Iceland is quite easy to do on your own. How long do you have off the ship to venture out? Your must-sees will entirely depend on that! There are some things you can easily see in a day and others where you need 3-4 days.
If you just have one day then you have some choices.
In my opinion, the Blue Lagoon is worth it! There is no other place like it on Earth, at least that I've seen. It's expensive but they only let a limited number of people in at one time so I didn't think it was crowded at all. The lagoon is very large and you will have plenty of room. If you go on your own, don't get the cheapest package...get the Premium Package. If you get the cheapest one you'll be waiting in line with all of the tour groups. The Premium line has few people and you go right on.
If you want to take a day and rent a car, then you can go out to the Golden Circle to visit Gulfoss Waterfall, see Geysir, and eat at Fridheimar - a tomato hothouse farm that has a very unique restaurant. Highly recommend!
Or you can just go to Reykjavik - there is plenty to see and the town is very cute.

I went to Iceland by myself at the end of a trip to France with my husband (he went back to work). It's a great country and I think it would be easy to venture out on your own, if you have done a lot of research and have a plan. We have only been on one cruise (Rhine River). It seemed like the optional excursions were really pricey and we opted to do our own thing most often, similar to what others were paying a lot of money for.

I did a golden circle tour. I enjoyed Gulfoss and Thingvellir very much and consider Thingvellir a must do. It's beautiful and has so much geographic and historical importance. The Geysir area paled in comparison to Yellowstone, but it was pretty. I didn't do the Blue Lagoon. It's expensive and man made. However, many people enjoy it, and Rick Steves recommends it. I would weigh it against your other opportunities. I would make sure you do a walking tour of Reykjavik, especially Harpa and Hallgrimskirkja. My recollection was that it was pretty inexpensive to go up to the top for the great views.

My main concern with that would be rough seas. See posts like this: https://www.tripadvisor.com/ShowTopic-g189952-i223-k11544575-Is_the_sea_rough_between_Northern_Scotland_and_Iceland-Iceland.html

Otherwise I am a huge cruising advocate. But everything I have heard about Iceland suggests it’s very easy to do on your own.

I'm not sure if you've already booked the cruise and would like more info about excursions or if you have yet to purchase the cruise.

Yes, I have already booked the cruise. So we will have limited time in port and I know some of the places are more remote, so might not have a lot of choices if we venture out on our own.

We are also going to Svalbard Norway. Any ideas for there?

We did the North Sea last year, so we are very familiar with "rough seas".

It sounds like you are a veteran cruiser. Perhaps you already have figured out this tip, but on rainy days, I wear a visor or baseball cap under the hood of my raincoat. It keeps the hood in place better and rain off my face. That came in handy when we had a rainy day on one of our cruise stops. You are correct, outside of Reykjavik things get remote pretty fast. If you plan to try any excursions on your own, I'd make sure to have transportation figured out in advance. While I'd prefer to venture out pretty often on my own, if there is nothing in the way of uber or sites are beyond what you can walk to, you might have to do their excursions.

If a Golden Circle tour is an option for Iceland on your cruise, that would be my first choice (if there is an all-day extensive tour available), as it would give you a chance to see the land, the geothermal natural aspects, as well as the industrial aspects of that natural resource, and the unique beauty. My second choice would be the Blue Lagoon. I was uncertain about it, but wound up truly loving it, as did my spouse.....exceptionally relaxing. If you can do both in your time there, definitely do both. I would not sign up for just a general city tour.....we did all of the above in our days there, and the city tour was not my favorite activity...nice enough, but not as interesting as the other two experiences. The opera house, which we saw only from the outside looks lovely.

I hope you see the Northern Lights (if you did not on your other earlier journeys North). Funny on our particular journey to Iceland and Greenland, I actually saw them out the plane about 15 minutes before landing in Iceland...the only time I have ever seen them!! We were on a National Geographic expedition that was land based in Iceland, then charter flight to Greenland, where it was then ship-based.

You will enjoy Iceland. It is different, for sure.

I've visited Iceland twice - on a TransAtlantic cruise (full day docked in Reykjavik) and also on a stopover for several days with Icelandair. During the stopover, we concentrated on exploring the Reykjavik sites as we could mostly walk everywhere, and really enjoyed the city attractions during beautiful August weather.

Prior to the Princess cruise, we booked one of the ship's excursions, which included pre-booked time at the Blue Lagoon, a special interpreter presentation at the Viking World Museum, and an interesting drive (with stops/walks) through the geothermal hot spots, black sand beaches and lava fields. The excursion content was excellent, however, it was a windy rainy day in mid-September so the time at the Blue Lagoon was a unique "foggy" experience. (As I recall, the sea was not too rough from Norway to Iceland and then to Scotland, but no one can predict the weather.)

I suggest you read up on what you most want to see and do for the day, and then decide if an organized tour will allow you to get the most out of your hours there. Personally, I would love to return to Iceland in the future and stay longer to see this fascinating country.