I wrote the blog post that trosebery posted above so just wanted to chime in with my thoughts. It has been several years since our cruise in the Baltics but it was a great experience and definitely one of our favourite trips. Our older daughter was 12 at the time but our younger daughter had just turned 6 a couple of weeks before the cruise. It was our first trip to Europe with the girls and it was a great introduction. We went on a Mediterranean cruise two summers later and in terms of overall experiences, the Baltics was much easier with young kids.
We started and finished our cruise in Copenhagen and loved the city! Copenhagen is a very walkable city, however, we took a hop-on hop-off bus on our first day to get around to some of the sights efficiently and get our bearings in the city (after that we walked everywhere). We saw the Little Mermaid statue, toured Amalienborg Slot (Palace), played in the garden at Rosenborg Slot (Palace), went on a canal cruise, walked around Nyhavn (my 6 year-old loved the colourful buildings), and went to Tivoli Gardens both pre and post cruise. The main shopping district, Stroget, is pedestrian only and there's a LEGO store there that was fun - also street entertainment.
The ports of call on our cruise were: Stockholm, Helsinki, St. Petersburg, Tallinn, Gdansk, and Oslo. Stockholm, Helsinki, Tallinn and Oslo we toured on our own. We hired a private tour guide for our two days in St. Petersburg and we booked a ship's tour for Gdansk. Gdansk was the only day on our cruise which did not go well. In the cities we toured on our own, we were docked right in the city and were able to walk off the ship and go about our day. We were docked a fair distance from Gdansk and I had read that traffic was often brutal so we booked a ship tour to avoid the worry of not making it back on time. It was raining that day and both kids hated being on a group tour which involved spending far too much time visiting amber stores so others could shop.
For Stockholm, Helsinki, Tallinn, and Oslo, I researched ahead of time to find activities that would satisfy everyone in the family. Due to time constraints we sometimes had to miss a must-see attraction but 6 year-olds can't generally be rushed from place to place! For example, in Stockholm we chose to visit Junibacken (the Astrid Lindgren/Pippi Longstocking museum) rather than the Vasa museum. Some day I'll get back to see Vasa but I thought it more important for my 6 year-old to have fun that day and leave with a positive impression of Stockholm. (I have articles on my website about all of the ports we visited if you're interested in the details of what we did in each city.)
My overall advice would be to tour most ports on your own or book a private guide who will design a family-friendly tour for you. We have found that it is often the case that hiring a private guide is no more expensive than booking 4 or more people on one of the ship's tours. If you are more comfortable taking a ship's tour then try to find one that is described as family-friendly.
Our Baltics cruise was on the Emerald Princess and we have sailed Princess two other times - the Diamond Princess in Alaska and the Crown Princess in the Caribbean. My younger daughter in particular loved visiting the kids club on our Princess cruises. There were lots of activities but there were not so many kids on the ships that the facilities were crowded. She enjoyed seeing the same kids every evening and on sea days and developing friendships.
A bit long winded but all to say that I think your entire family will enjoy the cruise in Northern Europe. Just be sure to plan ahead so you know what you intend to do in each port. Don't try to see everything as that will just exhaust everyone - go at a slower pace to accommodate the little ones and focus on having fun. 🙂
Happy to answer any questions.