In addition to the castle, the cathedral is another prominent landmark with its tall towers. It is also the archbishops seat, and the venue where the protestant reformation started in Nordics. The cathedral is still used on daily basis, so it is a bit hit or miss whether a visit is possible. When I visited, there was a christening taking place, but thankfully it was short and I was able to return bit later. There is also a crypt with an entry fee, but it was under renovation so visit was not possible.
Many Swedish Kings and Queens have had their coronations here until early 1700s, and some are buried in the cathedral as well. From Finnish perspective, the place is interesting as it has the first remaining shield of Finland there in a tombstone of a King (I have forgotten which one...)