Public Sauna or Spa in Stockholm?

Hello!

I have family coming to Stockholm in early June and they have asked to experience a genuine Swedish sauna. Can anyone recommend one to me? I don't know where to go! If there was a pool too (outside?!) that might be nice too but not essential.

Also, on a separate note, I would like to go somewhere for a spa and have a nice Swedish massage with my husband for our anniversary. Any recommendations? A little luxury (but not too expensive) would be nice.

Thank you all!