This museum is a rather interesting mash-up of archaeology and modern art. The latter is, well, not so interesting to anyone except maybe a specialist.
The archaeology is, however, rather impressively done, and by itself merits a visit to the museum. You get to step down into the underground excavation area and visit the remains of the medieval Turku. Displays are well-placarded in multiple languages (English, Swedish, Finnish). There are quite a number of stations explicitly designed for younger children which should keep them engaged during a visit as well. Altogether, I wished I had more time to spend there (a few hours, rather than the ~1 I had there).
This review is the subjective opinion of a TripAdvisor member and not of TripAdvisor LLC.