One of the few remaining museums that still is free to visit is the wonderfully situated Sjöhistoriska museum. Since you most likely want to visit the beautiful Djurgården anyway, why not pay a visit to Sjöhistoriska. The main focus is on shipping and the Swedish shipping history but they always have something fun going on. Get there on buss 69 or a nice walk along the canal from Djurgårdsbron.
Some other free museums in Stockholm are:
Kulturhuset, Riksidrottsmuseet, Stockholms läns museum, Tullmuseet
