Itinerary suggestions - Stockholm, Copenhagen, then ???

I'm not sure if your 10-12 days includes your flight to and from Scandinavia or not.
Either way, I wouldn't try to do more than two cities unless you really do have at least 12 full days on the ground, not including your arrival/departure days.
If you plan to go by train or fly between Stockholm and Copenhagen, it's at least 5 hours by train...about the same via air since you have to get to the airport at least an hour before your flight. By the time you get to the station/airport, board, disembark, get to your hotel and check in, that's a fairly full day of travel with a bit of time left in the evening.
If you do have 12 full days then I would definitely add Amsterdam.
Stockholm is a beautiful city and you can easily spend 2-3 full days here.
Copenhagen has more to see and 3-4 days are a good length of time for this city. The food scene here is especially interesting!
Amsterdam has the most to see so I would try to get in 3-5 days there if you can. Great bars and museums.

If you choose SAS to get to Stockholm, then look at 'open jaw' ticket arrangements, with departure from Copenhagen.

Arrive Stockholm - 4 nights
Train to Oslo - 2 nights
Train to Bergen - 2 nights
Fly to Copenhagen - 3 nights
Depart Copenhagen

I mostly agree with David that adding Oslo and Bergen to your itinerary would be a nice move BUT I would take the overnight ferry from Copenhagen. We did it last year and it was really fun and easy. Then you may want to take the train to Bergen (check out the website for Norway in a Nutshell). before taking another ferry back to Denmark. Enjoy!

I like David's plan a lot. Since Scandinavia is "out of the way" for the more southern parts of Europe, you're unlikely to get to the area on trips to other places. So, while you're going there, focus on destinations there. In a short trip like yours (and, by the way, all of mine), staying in one smaller area is a good way to have a better trip.

When you go from Oslo to Bergen, do it via the Norway In A Nutshell, a coordinated series of trains, boats, and buses. It takes all day, but you get spectacular scenery. You need to reserve parts of it in advance, but it's worth it. All the details (as well as all kinds of other help) are in Rick Steves Scandinavia, which you should purchase ASAP. In particular, you will need his tips on saving money in these potentially expensive places.

If you are visiting friends in Stockholm, I would imagine you would want more than 2-3 days. Stockholm has a lot to do and is a lovely city. It reminds me of Boston with the islands and ferries, etc. Stockholm also has some good Jazz. As Copenhagen is easier to get to on other trips, have you ever thought of heading north to Kiruna and the Arctic Circle? I really liked Umeå, but I was relaxed. In May, Swedes are starting to enjoying their woods and trails as the days are getting long. Sweden has a pretty coastline and the archipelago all the way up the coast. On the other hand, between Stockholm and Copenhagen is Eksjö, which had the largest preserved wooden old town of any town in Sweden. You don't have a lot of days, so I'd suggest you enjoy Sweden or at worst include Copenhagen. Save Amsterdam for another trip. The country of Sweden is worth 12 days on its own, IMO.

Dreaming of some wintry Scandinavian weather as it's sweltering hot here just at the moment.

You should use the ferry system as much as possible. All of these Baltic capitals were built to front the Baltic Sea so ferries replicate the way people actually traveled. One of the highlights of a visit to Stockholm is to see the archipelego that leads from the Baltic into the capitol. If nothing else, take a ferry to Tallinn and back (or a triangle that includes Helsinki), so you get a chance to sail through.

Also if you fly SAS, I believe your ticket entitles you to good offers for getting around the region (it did when we flew them). If you don't have time to ferry, you should also look at flights to get around Scandinavia - trains are expensive and not particularly convenient.

Hello Sue. If you will be at Europe a total of 10 days, I recommend going to Stockholm and Copenhagen. And you will have time for one or two day trips (via trains) from Copenhagen. Ride in the Express train from Stockholm to Copenhagen. I liked Stockholm and Copenhagen.