Thank you very much ! Is there much to see in the city center ?
And in case I would like to stay one night, what is the cheapest place to sleep ?
Stockholm is a very beautiful city and depending on what you are interested in, there are many sights in the city center. Just to name a few, there is the outdoor museum Skansen with many animals, the royal palace, the viking boat "Wasa" which was restored and is a museum now, the old town "Gamla Stan", "Stadshuset" from where you have a wonderful view over the city.
To see all the beauties of Stockholm you surely need longer, but I would say these are some of the nicest places
There are lots of hostels and backpackers in Stockholm, so I think for one night this would be the cheapest possibility.
Here is a link to a site where you can find lots of information about the hostels: