Was on second cruise on Constellation to the Baltic: in 2002- so some info maybe dated or different.
Dover is 1.5 to 3 hour bus transfer from London or LHR. depending on traffic and day. You can see the white cliffs from the ship- did not personally have time to tour area- and would not plan on it unless you arrive in town the day before by train fronm London. Being from the Midwest- the harbor activity kept me more than entertained to cast off- but you can try- as you have two days at sea to get over jetlag from flight from USA.
Oslo- docks in town easy five minute walk to trainstain- mall and palace, town hall and warf which has been converted to modern shopping mall/ resurant complex. Vigland Park is an absolute must. Scheduled tours are there 15-30 minutes (had taken the prior yearon land tour) - we took tram from the warf and spent 2 hours+ before the ship hoardes arrived. Also ship museums across harbor- water taxi is in front of cityhall if do it on your own-otherwise bus tour (signs advertise) from warf or from Celebrity.
Stockholm- ship about five minute bus ride to town center (new and across bridge to old town) -shuttles were set up for our cruise. Old town a must best seen on foot and explore small winding streets.
Helsinki-ship docked at comercial port and 20 minute shuttle bus ride to town square all major tourist attraction s and several local markets an easy walk from stop.
Did not take any Celebrity tours. Used Lonely Plant and self guided tours. We had been in Oslo the summer before.
St. Petersburg- Russia is a totally different story- unless you take Celebrity tours you need a visa- which is both a pain in the ass to get but $100 plus handling fees. Use the scheduled tours-The Hermitage is arguably the best Museum in the world ( I'm checking out the Lourve this fall again)-be sure to see it in one of the itineraries. We docked in the comercial port 30 minutes from the city-unless you are comfortable and trust local taxis- stick with the organized tours. I will be back in Russia for a Viking River tour to Moscow-the country is intriging and beautiful-50 years of Communist utopia has taken its toll-it is different and be tolerant- if you want it like USA -stay in the USA. Keep an open mind and roll with the frustrations- which you will encounter especially if you get visa and self explore-- it is worth it
Tallnin- easy walk or shuttle to old town-compact and quaint- also had the best shopping on tour- as Scandenavia is expensive due to taxes and even more so with the weak dollar. Swedes, Finns and Norwegians take ferries to shop here.
Rostock is a 20-30 minute train ride to town-Northen Hesiatic architecture also only sand beach (Warmunde) in Baltic is a 10 minute walk from ship if it is warm and sunn also European and topless.
Copenhagen is wonderful and easy to explore on your own. Tivoli Garden- it is were Disney got his ideas for Disneyland and 75 years older!
Did not stop in Lithuania or Gdansk.
Stronly recommend the Lonely Planet Scandinavian Countries covers most of the ports:
of Lonely Planet World Guide online.
Remember you cannot see the whole city in the 8-10 hours in port- just a good sampling-if you take a tour- leave a few hours to explore on your own I guarntee you will not be disappointed.