I agree with Trixi that the Scandinavia ports are great for independent sightseeing and easy to see because English is widely spoken and the public transportation is so convenient and reliable. (Also, unlike some of the port cities for the Mediterranean, you will dock within a 20 minute walk to the attractions in most ports instead of a 2-hour commute by car or train, so that is a big advantage from a time standpoint.) The Constellation looks like a nice ship, so that should be great. I'm not a big fan of shore excursions because we feel like we wait so long for the bus to load/unload, potty breaks, etc. then we are rushed through the attractions. My husband and I are in our early 40's and fairly active, so we like to use our shoe leather to explore on foot and feel that we have much more interaction with the locals and have a better feel for the culture of each port, so please keep that in mind when considering our recommendations. But you don't have to use much shoe leather in these ports because the attractions are centrally located or within reach by local transportation. Also, everyone has different interests (I love the art galleries and my husband doesn’t, so we sometimes see different sights), so it kind of depends on what you like.
Stockholm was wonderful we were off the ship as soon as the gangway went down (about 7:00 a.m.) and went into the old town (Gamla Stan) in Stockholm while the streets were void of tourists to do a walking tour we found in the Frommers book (probably also on their web site) that includes the royal palace along with a lot of other great sights and had a great time enjoying the beauty--I can't say enough good things about this port--without all the crowds. Then we took a 10-minute ferry ride to the Djurgården island (the ferries were very easy to find on the waterfront and ran regularly) and went to the Vasa Museum and to Skansen. We had great timing because the stores were opening at the end of our walk, and we got to shop some too. Then when all the tour groups were emptied into the old town to shop at the same time and the streets were crowded, we were off to our other activities. The Vasa Museum was just great (we liked it as much as the Viking Ship Museum in Oslo although I would also recommend a stop there), and Skansen is a park made up of buildings from previous centuries that have been set up like the buildings would have been in that century—fabulous!!!
Copenhagen is also a wonderful city. The Danes are very, very friendly. We were in Copenhage overnight and went to Tivoli Gardens at night and thought it was very charming; the lights were pretty and the shows were great. That was another location in which planning paid off for us because I toured the state apartments at Christiansborg Palace and toured Rosenberg Palace (houses the Danish crown jewels) in the same day; my husband went to the Danish Resistance Museum and the military museum--he really loves WWII history. We did two walking tours in Copenhagen too, and they were great. We went to the old waterfront (Nyhavn) that is pictured in all the photos of Copenhagen. If you want to tour any rooms at Christiansborg, you’ll need to plan carefully; you cannot access room at that palace outside of tours (unlike Rosenborg which is open and you can just run around), and you’ll need to go on one of the English tours. There’s a schedule on the Frommers web site, but I would advise that you confirm prior to sailing. The public transportation in Copenhagen is very good, but you will need a cab from the ship into town at about $10 US and the ride is just a few minutes. The cabs were readily available and took credit cards. At the end of the day, I rode the public transportation back to the front of Tivoli Gardens and took a taxi from there to the ship.
In Oslo, we took a ferry from the harbor (the ship docks very close to the ferry landing) to the Bygdoy peninsula. Then we went to the Norwegian Folk Museum (it's similar to Skansen in Stockholm--they're both great, but Skansen is a little better) and to the Norwegian Viking Ship Museum to see the really, really old ships. The ship museum here is small, so you won't need more than a hour or so there. Then I did a walking tour of Oslo with some friends from the ship while my husband went to the Resistance Museum. We also went to the Akershus Castle. One note—many of the museums closed in mid-afternoon, so it took some careful planning in this port. I do wish we had gone to Vigelandsparken. It didn’t really appeal to me on paper when we were planning our day, but everyone from the ship who went just raved about it.
You’ll also want to be sure to be on board for sailing into and out of Stockholm (the archipelago is very scenic) and Oslo for the fjords. The scenery is spectacular in this area. In all of the port cities, the architecture is wonderful, and the palaces and attractions are very accessible. We didn't have a lot of great shopping, meaning that the prices are not really low like they are in Italy or other European cities, but we were able to find some home decor items that were reasonable and lots of souvenir items.
In St. Petersburg, I don't think you can go wrong with Red October tours. In Tallinn, you'll probably just want to walk around and use a walking tour from Frommers or something like that. We loved the Frommers Scandinavia book; it’s really comprehensive.
I hope that helps you in your planning and will be glad to answer any questions you might have.