I need help with recommendations for Scandinavia in the last two weeks of August - I would love to see 3 -4 countries but knowing this is tight I would be fine with spending 2 weeks in any 2 countries.
I think a cruise is a good way to see the area. Maybe a seven day cruise with a few days in one country ahead of the cruise and a few days in another at the back end.
There are also ten day cruises that cover more countries. You don't want to go longer than that. It's better to arrive early and get adjusted to the time difference, see sights and build in some flexibility in case your flight is delayed or you miss a connection.
I did a quick search at vacationstogo.com and it looks like there aren't too many budget options left on the baltic cruises (only balconies left). You could duplicate the itineraries with the overnight ferries that frequent the region, but I'm not sure it will save you money - you would have to price it out.
The nice thing about a cruise is your meals are included, which can add a lot to the cost up north.
Normally, in Europe, I strongly recommend people plan trips that are about evenly divided between cities and rural experiences. Scandinavia, however, is an exception. There, with the exception of the Norway fjords, the best experiences are in the capital cities. The rural areas, while fine, are pretty much like rural Minnesota or Wisconsin.
So, the upshot is, you don't need to feel like you've covered a "country", but rather, a city or area. The cities are VERY human-scale and easy to traverse. Unlike Paris or London, you can get a good feel for each city in 2-3 days.
In two weeks, you could spend 2-3 days in 5+ locations. There are lots of combinations;
Copenhagen, Stockholm, Oslo, Bergen (fjords) would be a good slower-paced itinerary.
Copenhagen, Oslo, Bergen (fjords), Stockholm (fly SAS), Helsinki would be a good faster paced itinerary and could include two overnights on ships.
Flying open-jaw would be very helpful no matter which combination you choose. You can PM me for more specific information once you narrow the possibilities.
Simran, my partner and I have a two-week trip planned for June. We fly into Helsinki, spend two days there. Then a day in Tallin, and an overnight cruise to Stockholm. Three days in Stockholm, then train to Oslo. Three days in Oslo, two in the fjords, two in Bergen. We are flying out of Bergen. The multiple days in Stockholm and Oslo will allow us to get out of the city to see nearby sights. We are doing it all by Scandinavian rail pass.
Good luck in your travel planning.