Kristiansand - sorry, we were supposed to go last year but got diverted so I've no idea.
Oslo- I see from the port schedule that you will be berthed a little further out from the City Hall than we were. We were only there for an afternoon so we only had time to do one thing. Major sights are Kon-Tiki and the Viking Ship Museum reached by ferry from various points. We went to the Vigeland Sculpture park, by tram 12 (westbound) from City Hall to Vigelandspark stop. (It's a mad sculpture park, you see the 'angry kid' statue on postcards all round the city). There is a tourist info office by the city hall and you may be able to get a multi-ride tram ticket there (they also open an office at the cruise terminal but it gets very busy very quickly) We worked out that our 15 minute tramride was costing us £3 each! Be warned, I don't think there is a Norwegian word for 'cheap'. Tram 12 eastbound from City Hall will take you to the Central Station, but do note that the Nobel Prize exhibition Centre used to be Oslo West station until the 1980s.
Copenhagen - if you berth at Langenlinie Pier, everything is walkable. You are 10 minutes from the little mermaid statue, and we just kept on going via the Royal Palace and the main pedestrianised shopping street, until we got to Tivoli Gardens, which are near to the Central station. No trams I'm afraid. If you're at the new Freeport terminal, you may need to consider a shuttle bus, as it is further out.
Helsinki - We berthed near Wartsila shipyard, a 20 minute walk (there are buses) from the main harbour and market place (which is brilliant, I agree. Strawberries about the size of cricket balls). At the tourist office on the edge of the market place, you can get a one-day public transport ticket valid on everything, including the ferries to the fortress island of Suomenlinna. Trams 3T and 3B combine to form a circular (well, figure 8 actually) route which passes the station, the Rock Church and the Sibelius memorial among other places. A day card allows you to hop on or off as you please. (NB the Rock Church isn't a heavy metal place of worship, it is literally hacked out of the living rock. We were lucky and got there 15 minutes before a wedding party arrived. Because of the wedding several organised tour groups were unable to go in).
St Petersburg - as I said before, I can't fault DenRus for a tour company (no, I don't work for them). Comparing notes on the ship afterwards, we would have had to go on several of the (more expensive) ship's tours to see what we saw on their 'Complete St Petersburg' Value Excursion (2 day). There were plenty of chances to photograph the trams, we just couldn't ride on them, but we did get a ride on the Metro between two of the more ornate stations.
Tallinn - agree with moonrakerz, everything is walkable from the cruise quay and the old town is the place to be. The station is down below in the new town and contains a weird and wonderful array of ex-Soviet rolling stock. (Or it did, anyway. Things nmay have changed but I doubt it - railways don't seem to be seen as very important there). There are trams but I've not been on one, they only serve the new town. You do cross the line though, on the way from the ship to the old town.
Zeebrugge - went on the coast tram for the first time last October. A full day ticket cost about 5 euros. The most scenic stretch is south of Ostend where the line runs right on the sea front with the old German Atlantic Wall fortifications (read big guns) on the landward side. For the rest, I was surprised how little you can see the sea from the tram - either there are dunes cutting off the view or you are on a main street a block or two inland. It's still well worth 5 euros of anybody's money, if trams are your thing.
Writing this is bringing it all back. I'd go again tomorrow given the chance! Enjoy!