Also, the topic of the Blue Lagoon came up. Blue Lagoon can definitely be a "go"!
Although I can take you to less touristed hot geothermal waters as well. Even our "public pools" are really more like spas, and there's everything from "non-Blue lagoon formal spas" to hot springs and hot rivers in the middle of nowhere (and everything in-between).
Some examples, ranging from the formal and touristed to "middle of nowhere":
Blue Lagoon:
Jarðböðin (Earth Baths) at Mývatn:
Laugardalslaug "pool" - the biggest in Reykjavík. All "pools" are geothermally heated to swimming temperature and have hot tubs, steam rooms, etc along with them. The waters aren't blue (they lack the clay), but I actually prefer that (the blue waters make your hair unmanageable for a couple washings afterwards). You still get the sulfur smell. The blue waters at the more formal places are a nice aesthetic, though
Examples of smaller countryside "pools".
Then you get down to the things that are like little hot tubs built into the ground out in random places:
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Then you get into things that are just rocks placed across a hot spring, or natural pools, or places where someone ran a hose from a hot water source into a basin:
Then there's the "unusual", like hot cave springs:
Or volcanic calderas:
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