My last day in Reykjavik, I was keen to try a local pool. Especially as I hadn't been able to swim at the Blue Lagoon visit. I was really happily surprised at the facilities here. It took me 30 mins to walk down from the centre of the city, but worth it to see where the locals live. When I got in, the changing area was 'municipal ' but still clean & well supplied. I wish every pool had a spinner to take the water out of your bathers. The pool area is great, however. Multiple small dip pools at different temperatures, a large spa pool, an amazing steam room (which is big enough for people to use for yoga!), & 3x lanes to swim. Everything is close enough so you dont get too chilled as you walk between areas. Children well accommodated. Its I wish I'd sussed this out earlier. I'd only allowed myself an hour in there, which wasn't enough. I'd recommend all visitors to Reykjavik support this local geothermal pool & give yourself 2-3 hours.
For heavens sake, don't try to take photos. I noticed in other reviews that staff at pools were aggressive. Honestly, they value their privacy. Don't be the tourist that ignores the rules.