I am a Swedish immigrant to the United States and I have been back to Sweden many times with my family. I am also fairly well traveled otherwise. Therefore I think I can have an opinion on whether you should visit Sweden and what you should see.

There might be more interesting history and culture to see in Continental Europe, for example, in Paris, Rome, Greece, etc. However, if you have already been to Central and South Europe, or if you like the Northern cooler climates, or is more interested in Nature then Culture then Scandinavia and Sweden is for you. That is not to say that there are not a lot of culture in Sweden. There are a lot of old buildings and history to see in Sweden. It is just not as concentrated as in Continental Europe.

A few things that I think Americans would appreciate about Sweden are:
(1) Credit Cards are widely accepted (except Discover)
(2) Bathrooms and other amenities are clean and easily accessible
(3) People are quiet but there is very little hostility towards Americans.
(4) Most people speak English well
(5) The Currency (Swedish Crown + Euro) is easy to exchange inside and outside the country (you can change the currency back to dollars in the U.S.)

In summer I would recommend Stockholm, the Wasa Museum, Skansen, Djurgården, Gröna Lund, the Old City, the Nordic Museum, the Kings Castle and the national treasure chamber, Drottningholm the Royal summer Palace, as well as the Stockholm archipelago. Stockholm is built on Islands and is one of the most beautiful European cities in summer and the temperature in summer is comfortable.

Uppsala which is about 50 miles North of Stockholm is also an interesting town. Uppsala is an old medieval town with and a major University Town. Since 1164, Uppsala has been the ecclesiastical center of Sweden, being the seat of the archbishop of Uppsala. Uppsala is also very important in Norse Paganism due to Gamla Uppsala (Old Uppsala), an old Viking Capital. In Gamla Uppsala you can see Iron Age grave fields with Royal mounds, and you can drink tsty mead brewed from a 900 year old recipe and learn about the Vikings. The Walpurgis festival in Uppsala (April 30) is huge and a lot of fun.

In the North there is a lot of beautiful nature including the Scandinavian Mountains in the North West and the High Coast on the Bay of Botnia. Brown Bears (similar to Grizzly Bears) and Wolf are increasingly common in the North and Moose and reindeer are typically easy to spot. In the fall tourists can go Moose hunting.

Winter is not the best time to visit Sweden, however, if you do, the Ice Hotel in Jukkasjärvi near Kiruna North of the Polar Circle is a great spot for adventurers and kids. The Ice Hotel is made entirely of Ice and Snow and the lamps, chandeliers, the furniture, the glasses you drink from and the plates you eat from are all made of Ice. The Ice hotel is full of art and statues made from Ice, literally hundreds of amazing Ice art work. My kids loved to sleep in a pure snow and ice room, to play in the snow, go on a dog sled ride, and to see all the beautiful ice art, and O Boy what photos I’ve got.

I had to answer what time I went. However, I lived in Sweden for 24 years and I have gone on vacation in Sweden dozens of times, so that question does not apply to me.