Laugardalslaug is the most popular public swimming pool in Iceland. It's located in Reykjavik and is only 5 min from my apartment. It features a 50m outdoor pool, a 50m indoor pool, variety of hot tubs, cold tub, a sauna, a gym and a children's pool. It is open year-round with great opening hours. If you're staying a while I recommend buying a card with 10 tickets, you save a lot by doing that.