If you are spending the day in Copenhagen (having stowed your luggage) take a look at the day pass on the canal boats. A wonderful way to sit back & enjoy a very different view of the city - obviously weather can be a big factor though.
It would be good to know the exact itinerary to better help. If you are doing an overnight in St. Petersburg conside the Folk Dancing over the Ballet, we did this a couple of years back & had a wonderful time. Last year we did a combined full day tour to Peterhof & Catherine Palaces. In the sunshine they were both amazing, we were very lucky though as the time of year meant we have very few crowds and were given plenty of time to explore. On the following day we did a St.Petersburg On Your Own - the first time we had experienced being let off the leash, it was really enjoyable, well after we all got off the bus & looked around as if to say "are you sure we can?"
Look online for self-guide tours of most of these cities, there are some great walks for all age/mobility groups which allow you to pick & choose ahead of your visit.
Also look for free guided tours (they operate on tips on basis) One of the best groups we use are NewEurope and in the Baltics have used them in Copenhagen, Berlin, Amsterdam and Hamburg. They run separate groups (max 20 pergroup) depending on language needs. Usually English & Spanish.
For Stockholm, a bus will normally be laid on into the city centre, but again there are some hop-on/hop-off boats, and these pick up right behind the ships - you buy tickets at the bottom of the gangway.
If you are interested in ships & history, then the Vasa Museum is a must here, again check it out on line. If you are on the ho/ho boat, this is one of it's stops.
Please let us know the ports of call & cruise season for a better idea of what to suggest.
Alan & Katrina