Hi, went to a few of the places where you are visiting a couple of years ago. In Copenhagen you can walk into the centre pretty easily and visit Tivoli gardens if thats your thing. We went but there isnt much going on at Tivoli gardens. Stockholm is just a short walk to the centre too. Warnemunde is right by the railway station where you can get the train which isnt far and everyone else on the ship will go too ! I cant remember the name of the German city the train goes too but remember it was very picturesque, and cheap to travel to also. Your biggest cost will be St. Petersburg because you cannot leave the ship unless you go on the trips organised by the ship, unless you have a russian visa !! which takes 6 months to apply for. We were there for 2 days and did 3 trips. Although a little costly and very tiring were well worth it. St Petersburg has beautiful palaces and the Museum is great too. Try the Vodka at about £3 per bottle !!
By checking out each place before hand and a little investigation you can do many things without ship excusion costs.
I hope you have a wonderfull time and I wish I was coming along too.
Copenhagen - Go into the town centre, head for the main canal (for directions, the majority of the locals all speak good English or ask for a map from the Excursion desk on board) and take a waterway tour - excellent way of seeing the local sights (including the Little Mermaid, we couldnt believe how small she is!). Helsinki - Good shops, bars and vibrant market on the waterfront. Again it is well worth taking one of the boat trips on offer here. Warnemunde - Within easy walking distance of berth. DONT take the harbour boat trip, its awful (unless you like seeing decaying, rusty Eastern European warships from the Cold War). Really nice market, shops and restaurants along the canal bank but when you cross the bridge into town, carry on straight ahead and there are some lovely shops/churches/restaurants/bars in the backstreets. You can also catch a train to Berlin from here. St Petersburg - take the ship organized excursions only, dont bother getting an individual visa - its definitely not a place to 'wander around' on your own. I agree with Mr/Mrs Thomas, the Vodka is a must, as is a visit to Peterhof Palace. Enjoy.