I briefly worked for a company at this little island, Skeppsholmen [1], a while back. It's beautiful and fairly hidden/quiet, despite being in central Stockholm. There's a hostel ship you can stay at too [2], which I highly recommend if you are in Stockholm on a budget. The Museum of Modern Arts [3] is quite good too, as far as museums in Stockholm go. As well as the Vasa Museum, which people have already mention.
1: https://en.wikipedia.org/wiki/Skeppsholmen