sweden and denmark in 2 weeks

My own experience outside of Copenhagen and Stockholm are limited, but I will give you what I know. Outside Copenhagen is Helsingor. It's a wonderful town with a castle that Hamlet was based on. It can be a daytrip, but would make a great overnight too. Also outswide Copenhagen is Roskild. There is a great Viking ship museum there, as well as the cathedral where all Danish royalty is buried going back to about circa 900. That is only 30 minutes by train from Copenhagen and so makes a very easy daytrip. There are numerous rural areas throughout Denmark that have quaint towns and can make a base for easy bike rides (everything is flat). RS mentions the Island of Aero in his guidebook, but really there are similar places all about. Some guidebook research will reveal the best and most attractive to you personally. With Stockholm, I suggest a different tact. Take the ferry to Tallinn, Estonia if you want to see Medieval character. It has very intact Medieval walls and city center, plus Russian history. The overnight ferry will take you through the Stockholm archipelago, which is not to be missed. Such a trip could also be combined with Helsinki, Finland. Doing just Tallinn would take 3 nights minimum (including the ferries). Adding Helsinki would add at least another night.

Odense, about 1.5 hrs. from Copenhagen, is a delightful town with a buried Viking ship museum, a recreated iron age village with lots of activities, and the open-air Funen Village, recreating life in 1800. Also, Hans Christian Andersen's house and a nice castle.

Thanx for replies. This time I'm seeing around Stockholm and another places in Sweden. I want to save a ferry ride from Stockholm to Helsinki and Tallinn for a next trip. I'd heard Visby is a nice place and popular for a medieval town. Also, RS recommends Kalmar (plus Växjö) as stopping places between Copenhagen and Stockholm.
If I cannot go both Visby and Kalmar because of the limited duration, which one is the better?

Never been to Visby, though I hear wonderful things about it. Kalmar is not medival, but it's a very nice town. From there we drove to Oland Island (perhaps a bus goes there too?) - very wonderful island with many stone ruins.

I've been to both Kalmar and Visby and I did prefer Visby. I don't think I'd go to Visby as a day trip though. It takes about 4 hours to get there from Stockholm when you count the local train to the port and the boat. I do think it is really lovely to spend the night so if you want to visit, consider staying there. A good day trip from Stockholm is to Mariefred. In Mariefred, you will find Gripsholm Castle. The town of Mariefred itself is also cute. You mentioned that you are going in mid-June. Keep in mind that in Sweden the Midsommar celebration takes place from June 22nd to 23rd and lots of things are closed while Swedes go out to the countryside to celebrate. If you happen to be in Stockholm, Skansen has many activities (Folk dancing, food, etc.) and is a good place for a tourist to spend Midsommar.

Stockholm has a couple of things to check out, and so does Skåne, but you'll probably get better value by doing things closer to Copenhagen. In Stockholm, there is Uppsala, Sigtuna, and Birka which are all historical. Uppsala is the old seat of power in Sweden, and has an early Swedish castle as well as Viking burial mounds. These mounds originally led some inventive Swedes to think that Uppsala was the heart of Atlantis (seriously). Today, there is a visitor center there with artifacts from the mounds and you can hike up to the top of them to see the Swedish country side. The town itself is very nice and is also home to Uppsala University, which is one of the best schools in Sweden for liberal arts. Sigtuna is closer to Stockholm and easily accessible by public transportation. Take the commuter train to Märsta and then a bus to the town itself. Sigtuna was a viking capital with about a thousand years of history. There are a couple of old church ruins in the town and it's actually quite picturesque.
Birka is the site of a viking city that was founded sometime around 700 AD. It was a huge trade post, but it was destroyed during the course of history and partially by changing water ways (if I remember correctly). In place of a bustling city, farm land eventually took over but every so often treasure from the viking city would turn up while people were working the land. Archaeologists in the late 1800s took interest in the area and today there is a museum, a recreated viking village (oriented towards kids), and beautiful landscape there. The real bonus is that the main way to get there is by boat, which is a great trip.