Aside from the normal try: the Stadsbiblioteket (national library) on Odengaten. Designed by Gunnar Asplund in 1924-8 a stunning series of spaces lovingly used and preserved. The same architect designed the Southern Cemetery (Skogskyrkogården with metro stop of same name): the chapels are in use so access is difficult although the landscaped grounds are beautiful and reflective.

Asplund worked with Sigurd Lewerentz on the cemetery: the latter designed one his two great churches in southern Stockholm: Markuskyrkan at Bjorkhagen (1958-60): one of the great post war buildings.
If you liked the dark brick modernist space of Markuskyrkan then try Celsing's St Tomas kyrka at Vällingby (1951). Both these churches are right by the suburban metro stops.

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