My parents and I are planning our second trip to Europe Next year and want to hit Scandinavia. We plan to go in July for about 16-18 days. We want to fly from Seattle to Reykjavik and spend the night there. The next morning fly to Copenhagen and spend 3 days there and a day trip to Aero. Then take a ship to Oslo and spend two days there and a trip to the fjords and spend the night in Bergen. Then take a boat to Stockholm and spend two days there and then go to Helsinki on the night boat. Spend two days in Helsinki. Then go to St. Petersburg for 4 days and then take a train to Tallin a day. Then fly home. I know this may sound crazy, but last year we hit six countries in two weeks. So I think we can do this.
Are you sure there's a boat between Bergen & Stockholm?
I'll bet there isn't. Maybe Bergen to Hirtshals, then drive/ride, then Fredericshavn to Goteborg, then drive/ride to Stockholm. You could probably walk/swim almost as fast.
While it has been a long time since I visited Aero, I think it would be an awfully long day trip from Copenhagen. The train ride was several hours and then you have to take a ferry over to the island. I doubt that you will take a boat from Bergen to Stockholm (and even if you could, it would be an extremely long boat ride); this is either a 14+ hour train ride or a 2 hour flight. I'd also suggest that you look at how you are connecting the Baltic capitals to reduce your travel time. For example, you might want to travel Stockholm - Tallinn - Helsinki - St Petersburg to take advantage of the short boat ride between Tallinn and Helsinki. I'm not sure you have really taken into account the vast size of Scandinavia and the Baltic region and the very long travel times between the places that you are visiting. In your current plan you will be spending a great deal of time on trains and boats and very little time enjoying the great sights.
Daytrip to Aero isn't doable from Copenhagen. It's not a quick trip. I would confine your daytrips to Northern Zealund (Roskilde, Helsingor) or across the water into nearby Sweden. If you do Aero, I would think of it as most of two full days with a night in Aero. Personally, I would trade a day in Aero for a day in Uppsala (near Stockholm), it has better history plus a university. Bergen to Stockholm is the same. Oslo to Copenhagen alone is a long overnight boat ride. This would be a good leg to find a flight, you will save days. St. Petersburg is great. You need a visa for Russia. I explored some train trips from Helsinki to St. Pete's that were part of an organized tour (saving the cost and hassle of Russian Visas), they are generally sold to Finns. We chose another option so I never fleshed out the details.
No boat from Bergen to Stockholm. Fly SAS Airlines. They have some nice bargains for a variety of city-to-city trips within Scandinavia. When we went, this was our route; Reykjavik-Copenhagen-Stockholm-Arctic circle train to the Norway coast-Trondheim & north fjords-Bergen-Oslo-back through Stockholm to catch the ship to - Helsinki. It was 21 days. If we had cut out the arctic circle part and flown from Stockholm to Trondheim (or Ålesund) it could have been done in 18, but without St. Petersburg. With St. Pete., you will have to cut something out. For example, fly from Reykjavik to Bergen and travel strait east (and omit Denmark).
Lots of good advice so far. My thoughts: Skip Aero and day trip to Roskilde or Helsingor - Roskilde for viking ships, Helsingor for a quiant 17th/18th century town and Kronborg Castle. Consider a flight from Copenhagen to Oslo though the ship could be pretty. Just don't sacrafice time since you'll do other boat rides. Definitely fly from Norway to Stockholm. Take night ferry from Stockholm to Tallinn. Take 90 minute ferry from Tallinn to Helsinki. Take train from Helsinki to St. Petersburg. Fly home from there or back in Helsinki. St. Petersburg can only be done with visas and the process is time consuming and beauacratic and very specific.
As an alternative to what Douglas said about flying, there's a night ferry that runs the Copenhagen-Oslo route. It'd probably cost you a couple hundred bucks for the crowd and, if you left at five or so, you'd get in by mid-morning. It's a darn long ways and the cabins are tiny (stacked shelves for beds). The common decks can get rather rowdy and sometimes the party continues into the cabin passageways. Directferries.co.uk probably has all the scoop.
Randy reminded me. We flew last summer into Copenhagen on SAS, they offered me a special rate on any other SAS flights within Scandinavia. We didn't use them but they looked like a good deal.